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					Moves in Mind




Board games have long fascinated as mirrors of intelligence, skill, cunning,
and wisdom. While board games have been the topic of many scientific
studies, and have been studied for more than a century by psychologists, there
was until now no single volume summarizing psychological research into
board games. This book, which is the first systematic study of psychology and
board games, covers topics such as perception, memory, problem solving and
decision making, development, intelligence, emotions, motivation, education,
and neuroscience. It also briefly summarizes current research in artificial
intelligence aiming at developing computers playing board games, and
critically discusses how current theories of expertise fare with board games.
Finally, it shows that the information provided by board-game research, both
data and theories, have a wider relevance for the understanding of human
psychology in general.

Fernand Gobet is Professor of Psychology at Brunel University, West London.
He is an international master of the International Chess Federation and has
played for several years with the Swiss national team.
Alex de Voogt is at the University of Leiden and Managing Editor of the
journal Board Game Studies.
Jean Retschitzki is Professor of Psychology at the University of Fribourg.
He was elected President of the Swiss Society of Psychology in 1998.
Moves in Mind
The Psychology of Board Games




Fernand Gobet, Alex de Voogt, and
Jean Retschitzki
First published 2004
by Psychology Press
27 Church Road, Hove, East Sussex BN3 2FA
Simultaneously published in the USA and Canada
by Psychology Press
270 Madison Avenue, New York NY 10016
This edition published in the Taylor & Francis e-Library, 2004.
Psychology Press is a member of T&F Informa plc
Copyright © 2004 Psychology Press
All rights reserved. No part of this book may be reprinted or
reproduced or utilized in any form or by any electronic,
mechanical or other means, now known or hereafter
invented, including photocopying and recording, or in any
information storage or retrieval system, without permission in
writing from the publishers.
This publication has been produced with paper manufactured to strict
environmental standards and with pulp derived from sustainable
forests.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data
Gobet, Fernand.
   Moves in mind : the psychology of board games / Fernand Gobet,
Alex de Voogt, Jean Retschitzki.
      p. cm.
   Includes bibliographical references and index.
   ISBN 1-84169-336-7 (hardcover)
   1. Board games—Psychological aspects. 2. Cognitive psychology.
I. Voogt, Alexander J. de. II. Retschitzki, Jean. III. Title.
   GV1312.G63 2004
   794—dc22                                              2004008865
ISBN 0-203-50363-5 Master e-book ISBN



ISBN 0-203-59526-2 (Adobe eReader Format)
ISBN 1-84169-336-7 (Print Edition)
To Chananda
FG

To Abdu Foum
AV

To Angoua Kouadio
JR
Contents




  Preface                                                          xi
  List of abbreviations                                           xiii


1 Introduction                                                      1
  Moves in mind 1
  Board games and cognitive psychology 2
  Role of board games in science 5
  Role of board games in psychology 6
  Structure of the book 9

2 Formal analyses of board games                                  11
  Fundamental concepts 12
  Board games in computer science and artificial intelligence 13
  Information and complexity analysis 25
  Game theory and the concept of error 27
  Conclusion 28

3 Theories of board-game psychology                               31
  Brief history of board-game psychology 31
  Theories of chess skill 33
  Influences from other theories of cognition 45
  Theories of development and environment 47
  Conclusion 49

4 Perception and categorization                                   51
  Low-level perception 51
  High-level perception and categorization 59
  Conclusion 66
viii    Contents
 5 Memory, knowledge, and representations                                 69
       Memory for board positions 70
       Recall of sequences of moves and of games 81
       Estimation of the number of chunks in LTM 86
       Mode of representation 88
       Representations used in blindfold playing 91
       Knowledge and memory schemata 95
       Discussion 99
       Conclusion 104

 6 Problem solving and decision making                                   105
       Empirical data on search behaviour 105
       Empirical data on the role of perception in problem solving 117
       Empirical data on the role of knowledge in problem solving 119
       Analogy formation in novice players 123
       Theoretical accounts 123
       Discussion 126
       Conclusion 130

 7 Learning, development, and ageing                                     133
       Early stages of learning 133
       Development of play and game behaviour 138
       Developmental studies of specific board games 140
       Ageing 149
       Conclusion 152

 8 Education and training                                                155
       Introduction 155
       Board-game instruction and the transfer of skill 156
       Teaching the rules and basic instruction 163
       Training and coaching at an advanced level 165
       Conclusion 168

 9 Individual differences and the neuropsychology of talent               171
       Intelligence and visuo-spatial abilities 172
       Personality 178
       Emotions and motivation 178
       Board games and neuroscience 180
       Conclusion 186
                                                              Contents    ix
10 Methodology and research designs                                      187
   Definitions of expertise 187
   Game specificity 189
   Illiterate games 190
   Ecological validity 190
   Cross-cultural aspects 192
   Creation and use of archives and databases 192
   Observations and natural experiments 196
   Interviews and questionnaires 196
   Introspection and retrospection 196
   Protocol analysis 197
   Standard experimental manipulations 198
   Neuroscientific approaches 200
   Typical research designs 201
   Mathematical and computational modelling 202
   Weaknesses and strengths of methodologies used in board-
      game research 203

11 Conclusion                                                            205
   Board-game complexity 205
   Landscape of board games 206
   Impact of board-game research 206
   Future 207


   References                                                            209
   Appendix 1: Rules of board games                                      237
   Appendix 2: Measures of expertise in board games                      247
   Appendix 3: Example of protocol analysis                              249
   Author index                                                          253
   Subject index                                                         261
Preface




At the end of a workshop on the ‘Psychology of Expertise’ held in September
1999 in Fribourg, Switzerland, during the Sixth Meeting of the Swiss Society
of Psychology, the three authors discussed the possibility of writing a book
that would bring together the available literature on the psychology of board
games. We had already carried out extensive empirical research on a specific
board game (chess for Gobet, bao for de Voogt, and awele for Retschitzki),
and found that an overview of the available literature would allow more
psychologists to appreciate the accomplishments and perhaps join in the
enthusiasm for this field.
   There has been no single volume summarizing psychological research into
board games. Monographs on scientific psychology exist for chess, but not
for other board games. For these other games, interested laypeople have to
carry out their own search through the scientific and board-game literature. A
difficult task, given that many publications are not issued in the mainstream
literature or even in mainstream languages.
   For better or worse, the literature appears dominated by chess research. We
were actually surprised, and disappointed, to discover the extent of this
imbalance. One consequence of this situation is that we could be relatively
selective for the inclusion of chess material, but much less with other board
games. While we have carried out an extensive search to identify work in non-
chess games, it is likely that we have missed some pertinent papers or books,
in part due to language barriers. For example, documents on the psychology
of Go and shogi written in Japanese may have skipped our attention. We
invite comments and pointers to aspects of the literature that have not been
included in this book.
   This book owes much to the assistance of colleagues in our own research
projects and also to others in its recent preparation. Previous collaboration
of the individual authors with psychologists in the field is found in detail in
the list of references. Such works include collaborations with Adriaan de
Groot and Herbert Simon, who will be discussed at length for their ground-
breaking work. We owe some colleagues and friends particular thanks
for their assistance with this book. Guillermo Campitelli, Peter Lane, Julian
Pine, Jos Uiterwijk, Chris Vincent and Arie van der Stoep were most helpful
xii   Preface
either with their commentary or by providing us with the necessary
references. Some colleagues from other fields commented on chapters or pro-
vided the necessary moral support, and in this category we need to mention
Luuk Reurich and Mickey Red. Nigel Pitt and Gareth Williams proofread
the final manuscript. We also thank the Swiss Journal of Psychology for allow-
ing us to reprint the material in appendix 3. Then there is a group of people
not mentioned in the references but whose participation in the research has
been a valuable contribution: players from all over the world have given their
time and effort to provide us with experimental data and useful information.
We cannot thank them enough.
   Board games have permeated almost all parts of psychology including
those parts that go beyond our joint expertise. While this book concentrates
on cognitive psychology, much material outside this field was included or
consulted. We hope that the reader will find reading this book as instructive
as we found writing it. We most of all express the hope that this book will
encourage further research in psychology, in particular in games where such
research is still in its infancy.
List of abbreviations




IQ   intelligence quotient (used as a measure of intelligence in intelligence
     tests)
LTM long-term memory
ms   millisecond
s    second
STM short-term memory
USCF United States Chess Federation

(Please see the index for the acronyms of computer programs and psycho-
logical theories.)


Stylistic conventions
We write ‘Experts’ (with uppercase ‘E’) to refer to players below master level,
and ‘experts’ (with lowercase ‘e’) to refer to skilled individuals in general.
  Board games are written with a lowercase letter (e.g., chess, bao), except for
Go, Othello, and trademark games.
1      Introduction




Moves in mind
This book is the first systematic study of psychology and board games. The
main purpose is to show the potential of using board games in cognitive
psychology and related disciplines by providing an overview of the available
literature, and insight into the properties and possibilities of these games.
   Board games have been used in psychology since Alfred Binet, the founder
of experimental psychology in France, studied blindfold chessplayers at
the end of the nineteenth century. His work anticipated aspects of modern
cognitive psychology and dominated the discussions of the early part of the
twentieth century. Fifty years later, chessplayers would be part of another
groundbreaking study when Dutch psychologist Adriaan de Groot con-
ducted his experiments on the thinking of chessplayers, including grand-
masters and even world champions. This work and the more influential
studies by Herbert Simon, who elaborated on de Groot’s experiments, have
dominated research on perception, memory, and problem solving to this day.
   The seminal works on chessplayers have been generalized to other domains
of expertise. At the same time, the domain of board games has received
attention in its own right from other disciplines. Games such as Go, gomoku,
bao and awele have enabled comparative studies that put theories of cogni-
tion in different cultural contexts. These studies would not have been possible
without an increasing interest in board games as an object of study.
   Psychological research on board games is found from disparate sources
ranging from journals on cognition to historical works on board games.
An overview of board games as it is used and understood in a particular
discipline exists for the field of artificial intelligence (Fürnkranz & Kubat,
2001) and computer science (Allis, 1994; van den Herik & Iida, 1999), and
such an overview was long ago provided for historical research (Murray,
1952). Fifty years after Murray’s seminal work, this present book provides
the first integrated study on board games and psychological research. It
shows how psychology theory and methodology have been influenced, and, in
the case of expertise, dominated by research on chess and other games. While
the historian may concentrate on the rules of a game or the career of a player,
2   Moves in mind
and the computer scientist may focus on the computational aspects of moves
and rules, the board-game psychologist now studies the moves in the player’s
mind.


Board games and cognitive psychology

Definition of board games
Psychologists have not always been explicit about the definition of a board
game. The definition of a particular game is generally considered understood
or otherwise transparent by listing the rules of the game. The choices and
assumptions that researchers have made prior to presenting their research on
games could bring us towards a definition of board games more appropriate
for psychological research. Such a definition is based on two characteristics
of board games. First, it is concerned with rules. Board games are games with
a fixed set of rules that limit the number of pieces on a board, the number of
positions for these pieces, and the number of possible moves. The limitations
set by these rules contrast with games of skill where the number of positions
may be endless. Second, there is indeed a board with pieces on it. This aspect
also states that moves or placement of pieces may influence the situation on a
board and that pieces relate to each other on a board. This is in contrast with
most lottery games, such as roulette, where each bet or contract is commonly
independent from the other contracts that have been made on the table, and
by definition are not moving around the board.
   Due to these two elements, board games contrast with games of skill, which
have endless positions; lottery games, which consist of placing a bet; and card
games (such as bridge, mahjong, and dominoes), which use cards instead
of pieces but do not need a board. Lottery games require a randomizer, such
as dice or a spinning roulette wheel, which determines the outcome of a
betting contract. A die in a board game only limits the movement of the
pieces. In terms of psychology, lottery games attract psychologists interested
in gambling and decision making under uncertainty, while board games
present opportunities for studying perception, memory, and thinking. Card
games do not seem to add a characteristic not already present in board or
lottery games, and so far relatively few card games (mostly bridge) have
entered the literature of cognitive psychology.
   All these games require players, and, in general, the number of players is
two. This sets them apart from puzzles, which rarely involve more than one
player. There are also possibilities for research on board games involving
more than two players.

Knowing: Degree, time, and context
For the purpose of this book, cognitive psychology may be defined as the
study of information processes enabling knowing, where knowing varies in
                                                                Introduction   3
degree, time, and context. Degree, time, and context are limited by the
contrasts between novice and expert, between child and adult and, to
some extent, between cultural contexts. Additional materials from clinical
psychology, artificial intelligence, mathematics and computer science may
also be mentioned but are not central to the studies presented here. The
contrasts themselves require definitions, and are highly problematic, as will
become apparent when theories and studies are discussed.
   Expertise, a dominant concept in most of the cognitive psychological
literature on board games, may be defined as the ability of individuals to
perform at levels consistently higher than the majority. Research into expert
behaviour in a number of domains, including mathematics, physics, sports,
medicine, and art, suggests that the same mechanisms underlie diverse
types of expertise, although the detail of these mechanisms is disputed by
theorists (for overviews, see Chi, Glaser, & Farr, 1988; Ericsson, 1996;
Ericsson & Smith, 1991). One of the main topics of this book will be to
identify the psychological processes enabling some players to excel in their
game, and to compare these processes with those identified in other domains
of expertise. (Appendix 2 discusses different measures of expertise in board
games, and Chapter 10 analyses the methodological implications of these
measures.)


Classification of board games
While so far ignored or scarcely used in psychological research, a classifica-
tion and description of board games allow a wide range of research possi-
bilities. A classification is necessarily dependent on its purpose. In the case of
psychology, this purpose relates to the cognitive aspects of a game that needs
clarification in relation to other games. Such a classification appears to be not
much different from that used for historical or anthropological purposes as
made by Murray (1952) and is almost identical to that from a players’ point
of view as presented by de Voogt (1995).
   War games include chess, Go, bao, draughts, and most other games in
which the destruction of the opponent is the main object of the game. These
games are commonly competitive, and therefore dominant in cognitive
research on expertise. In race games, the object of the game is not to destroy
but to reach a target for which capturing pieces of the opponent is only one
means to an end. Race games frequently include dice and are rarely played in
competition because of this element of chance. Backgammon is an important
exception, but has rarely been used in cognitive research. Alinement games
concern games where captures are not made and dice rarely play a role.
Examples include gomoku, tic-tac-toe, and pegity. They require players to
place their pieces, and reach a configuration. The difference with race games
consists in the placing of pieces on the board rather than moving pieces
across the board. These games are also played in competition, and since they
rarely involve dice, they have frequently appeared in cognitive psychology.
4   Moves in mind
Alinement games can be seen as race games in which the target is a con-
figuration; moves around the board and randomizers do not need to play a
role.
   Competition is mainly required for research on expertise. In the case of
development, education and cross-cultural studies, there appear other con-
cerns such as classifying the rules according to their simplicity and avail-
ability. While some have chosen strategically complex games (chess, Go, bao)
to gain insight into experts’ thinking processes, others have selected board
games for the simplicity of their rules (pegity, tic-tac-toe, checkers, awele,
and again Go) to involve the youth in developmental studies or have easy
access to novice players compared to expert players. If the rules are not
simple, then most researchers switch to games that supposedly need no
explanation for the audience for whom the research was presented (chess,
checkers, shogi, Monopoly). In addition to using simple rules or known
games, some games (chess, Mastermind, Go, gomoku) were modified or
simplified to suit the needs of the researchers.
   The elements of degree, time, and context in cognition each requires a
different type of board game. When played in competition, war and aline-
ment games are used in the study of novices and experts. Developmental
studies prefer simple or simplified games, with most psychologists preferring
known games to games that require extensive explanation. This division has
become most striking in cross-cultural studies where known games appear
greatly different from one area to another, where simplifications are not
always acceptable, and where competition is not always registered in ways
similar to systems known in the literature. These differences in systems of
competition are explained later in the book but the difficulty of comparing
games that are played in different contexts remains and points to possibilities
for future research.


Organizations
Competitive board games, including chess, Go, and checkers, are represented
by organizations at the national and international levels. Locally, associ-
ations of players and clubs offer opportunities of training to different levels
of players, publish newsletters and journals, make available books and
equipment, and organize promotional activities and tournaments. Some
tournaments, such as the Mind Sports Olympiads organized annually in
London, put together different games, including board games.
   The presence of organizations has enabled the creation of archives and the
development of considerable knowledge, including analysis of openings and
endgames, investigation of strategic plans in the middlegame, and collections
of typical combinations. Many of the implications of organized play are
discussed in Chapter 10.
                                                              Introduction   5
Role of board games in science
Board games have intrigued researchers in a number of sciences, either as
objects of study or as models for developing analogies. The following review
shows which role board games have taken up in the individual disciplines.
Such a review is more suggestive than exhaustive due to the extensive nature
of the material.


History
The systematic and historical study of board games outdates the study of
psychology. The first descriptive works by Hyde (1689, 1694), Falkener (1892),
and Culin (e.g., 1893, 1895), to name a few, were followed by even more
detailed or comprehensive works in the twentieth century by Bell (1960) and,
most notably, Murray (1913, 1952) in English and Lhôte (1994) in French.
   These board-game studies focus on the development and dispersal of
board games. History is thereby much aided by the fields of archaeology
(e.g., Schädler, 1994, 1995), linguistics (van der Stoep, 1997), art history
(e.g., Faber, 1994; Walker, 1990), and philology, which in turn can be split
into Egyptology (Rothöhler, 1999), Assyriology (Finkel, 1995), Indology
(e.g., Bock-Raming, 1995), Sinology (e.g., Eagle, 1998; Röllicke 1999),
and other regional specializations. Board-game studies have become an
interdisciplinary field (e.g., the study of board-game dispersal: Eagle, 1998;
Kraaijeveld, 2000; de Voogt, 1999).
   Murray summarized ethnographical mentions in his books on board-game
history. With the notable exception of Townshend (1986), anthropologists
appear almost absent in the board-game studies literature. Instead, the social
sciences developed a different focus.


Social sciences
Sociology (e.g., Sutton-Smith, 1997) and anthropology (e.g., Malinowski,
1944) developed an interest in play rather than board games. The idea
of Homo Ludens and the element of play in a culture was first introduced by
the Dutch historian Huizinga (1938) and has found a wide following in the
social sciences. Although board games are sometimes mentioned, they are
hardly popular objects of study or even analogies of much significance. Three
exceptions to this rule may be mentioned here. Wendling (2002) discusses
chessplayers’ ethnology. Dextreit and Engel (1981) address the links between
chess, on the one hand, and politics and military science, on the other.
They also carry out a sociological analysis of the chess world, and discuss the
links between chess and advertising. Finally, Boorman (1969) proposes an
interpretation of Mao’s strategy in terms of Go.
   In economics, the field of game theory studies decision making under
situations of conflict (von Neumann & Morgenstern, 1944). Contrary to
6   Moves in mind
what the name suggests, game theorists hardly focus on board games, with
the result that literature is largely absent, even on chess. The mathematics
involved in game theory could also classify this field as part of the sciences,
where the board-game situation is quite different.


Mathematics
Due to their well-specified rules, board games have been a favourite subject of
study in the formal sciences, in particular in mathematics. For example, in an
influential paper published in 1913, Zermelo used chess to formalize the
concept of game tree and introduce the method of backwards induction.
Board games have also been of interest in the field of combinatorial analysis
(Deshayes, 1976; Petkovic, 1996). Finally, board games (in particular chess,
checkers, and Go) have often been used to illustrate and investigate the theory
of emergence—how complex behaviour emerges from simple components
(e.g., Hofstadter, 1979; Holland, 1998).
   The studies of artificial intelligence and computer science have made
extensive use of board games, and have also influenced the field of
psychology. Therefore, a review of their research requires a separate chapter
in this book.


Philosophy
In philosophy, board games and games in general have occasionally been
used as analogies (Reurich, 1995). Seidel (1995) makes an analysis of the
syntax of propositional logic in comparison to chess. De Saussure (1916)
several times used chess to illustrate the rule-like properties of language. He
also drew an analogy between the development of a chess game and the
‘synchronic analysis’ of language; if one enters a room where a chess game
is being played, one can study and understand the current position without
having to know the moves leading to it.
   In some cases, the player rather than the philosopher wished to make
a contribution to this field. Chess world champion Emmanuel Lasker
(1905) developed a philosophical system called ‘machology’ (from the Greek
mache—fight, and logos—science), which erects the element of fight present
in a chess game as an overarching principle. Among other philosophical
systems based on chess, one can mention Seifert (1989), and Siebert (1956).
   Again we may mention artificial intelligence since board games have often
been employed in the philosophical debate over the possibility of artificial
intelligence; we will expand on this topic in Chapter 2.


Role of board games in psychology
Quantitatively, chess is the (board) game that has generated most research
in psychology, starting with the work of Binet at the end of the nineteenth
                                                                Introduction   7
century. Based on our literature research, mancala games as a group come
second, followed perhaps by tic-tac-toe. There is no systematic research
tradition for games such as Go or checkers, although there are a few
occasional research papers on these games.
   Board games have been most influential in cognitive psychology. In par-
ticular, the works on chess by de Groot (1946) and Chase and Simon (1973a,
1973b) has had quantifiable historical impact (Charness, 1992), and has con-
tributed to the development of several concepts, such as chunking, selective
search, and progressive deepening. A substantial part of this book will deal
with cognitive psychology. Recently, board games have been investigated
from the point of view of neuroscience.
   Board games obviously require players, and many games are played mainly
by children. One can therefore be surprised by the relatively small number of
studies devoted to developmental psychology. Rubin, Fein, and Vandenberg
(1983, p. 727) note that there has been less psychological research on children’s
game-oriented behaviour than on children’s play, and that the board-game
literature comes mostly from anthropological and sociological sources.
   There is also relatively little research on (board) games in cross-cultural
psychological research (Hopkins & Wober, 1973). For instance, mancala
games have been studied by ethnographers rather than by psychologists
(Hopkins, 1970). The first systematic observation of this kind of game was
presented by Cole, Gay, Glick, and Sharp (1971), who described the game
played by the Kpelle of Liberia.


Features of board games of relevance for psychology
Board games offer a number of interesting features from a psychological
point of view, including: well-defined domains and rules, a multitude of
potential tasks, and good ecological validity. In addition, some board games
come with a ranking system which makes it possible to measure expertise
quantitatively. Finally, with some board games, there is the possibility of
productive cross-fertilization with artificial intelligence and computer science.
   Some potential shortcomings must be mentioned as well. Some games have
complex rules; it may be difficult for the researcher to deal with the behaviour
from several players simultaneously; and communication with players may
be difficult in certain games (see Chapter 10). To alleviate some of these
problems, researchers sometimes simplify the situation by using only a subset
of the rules, or by considering only the choice of the best move in a given
situation, reducing the game to a problem-solving situation. Recent develop-
ments in information-processing technologies promise to mitigate some of
these shortcomings; for example, it should become easier to automate data
collection for a number of board games, the computers being able to play the
role of the opponent.
8   Moves in mind
Criticisms of the relevance of board games for psychology
Research using board games has been criticized as being of little interest for
psychology in general, because the population it studies is highly idio-
syncratic (e.g., Hunt, 1991). We believe that this sort of criticism is misguided.
In biology, studying ‘model organisms’, such as the drosophila (fruit fly), can
be a powerful means to gain knowledge that generalizes to a large number of
organisms. Indeed, Simon and Chase (1973) have proposed that chess is the
‘drosophila of psychology’, a role that Russian mathematician Alexander
Kronrod had suggested earlier for artificial intelligence (McCarthy, 1997).
Just as some features of the drosophila make it ideal for studying the laws
of genetics (e.g., size of its chromosomes, rapid reproduction cycle), several
features of chess make it an ideal environment for studying cognition
(e.g., quantitative measure of skill, crisp but complex microcosm). The real
question for ascertaining the value of using chess and other board games in
psychology is whether conclusions derived from these games generalize to
other domains. The fact is that concepts and mechanisms identified within
board-game research, such as progressive deepening, selective search, the
role of pattern recognition, and experts’ remarkable memory for domain
material, have been shown to generalize to most, if not all, domains of
expertise (Charness, 1992; Gobet, 1993b).


Board games in clinical and biological psychology
Focusing this book on cognitive psychology had the consequence of leaving
out of consideration a number of topics that are related to psychology
but beyond the authors’ expertise. We briefly mention them here, mainly to
provide the interested readers with bibliographic sources that will point
to further readings.


Psychiatry, psychoanalysis, and psychotherapy
While board games are often associated with intelligence and wisdom,
their practice is sometimes thought to be related to madness. Chess, in par-
ticular, has a substantial literature about a (putative) link with psychiatric
disorders (mainly schizophrenia), often with reference to the psychoanalytic
literature. Fine (1978) also uses psychoanalytic concepts to characterize
beauty in chess, which he opposes to the principles proposed by Margulies
(1977). Pointers to this line of enquiry can be found in Dextreit and Engel
(1981) or Fine (1967). Criticisms of this approach can be found in Holding
(1985).
   Less speculatively, Rey et al. (1996) report the case of a young man with
epileptic seizures induced by playing chess and Scrabble. The role of chess in
psychiatric treatment is addressed in Fleming and Strong (1943), Pakenham-
Walsh (1949), and Smith (1993). In this vein, one may also mention the use
                                                              Introduction   9
of checkers in child therapy, discussed by Gardner (1969, 1993), Levinson
(1972), and Loomis (1964, 1976).


Psychophysiology
The game of checkers also found some use in psychophysiology, such
as Vernoy (1989) who studied perceptual adaptation underwater, and
Manowitz, Amorosa, Goldstein, and Carlton (1993), who compared the
increase of uric acid level in humans engaged in gambling with money,
as compared with playing checkers without betting. Chess was used by Holck
(1933) to investigate the effect of caffeine on solving chess problems.


Popular psychology
Several books have been written about practical psychological techniques
and tricks, including cheating, that can be used in board games. In chess, such
information can be found in Chernev (1948), Hartston and Wason (1983),
Kotov (1971), Krogius (1976), Munzert (1988), and Pachman (1985). Odeleye
(1979, p. 51) described a few ‘psychological tactics’ about the mancala variant
called ayo: ‘By shouting at their opponents, calling them names, and hurrying
them to play, most skilful players are able to confuse their opponents who
because of this make mistakes which the skilful players are quick to recognize
and exploit.’
   De Voogt (1995) distinguishes three types of ‘deceit’ in the psychological
tactics of bao. Legal deceit refers to moves whose sole purpose is to confuse
the opponent rather than play a good move. Illegal deceit, as the name
suggests, breaks the rules and includes the misplacing of counters or
fumbling of counters to influence the outcome of the move. Such examples
were also found by Townshend (1986). Finally, setting change is considered
that part of deceit that is outside the board such as verbal or even physical
intimidation. The popular work on gamesmanship by Potter (1947) illustrates
this tactic at length for the game of golf.
   Most board-game publications on training and instruction do not have a
scientific basis, but we will see in Chapter 8 that research in psychology can
help improve current methods.


Structure of the book
Chapter 2 gives an overview of formal approaches to board games, including
computer science, information theory, and mathematics. The goal of the
chapter is threefold: to introduce some key concepts that are often used in
the remainder of the book, such as ‘search tree’; give an indication of the
complexity of the environments offered by board games; and show what
methods computer science and artificial intelligence have developed to tame
10   Moves in mind
this complexity. As we shall see later in this book, the differences between
these methods and those used by humans are instructive.
   Chapter 3 discusses the theories in cognitive psychology that have found a
wide application in board-game psychology. The basis of many of these
theories is found in research on chess, while other board games have tested
their wider application. Theories on cross-cultural and developmental
psychology are also discussed but their support appears not always based on
experiments.
   Experimental designs structure the chapters on perception, memory, and
problem solving. Chapter 4 discusses perception and the tasks developed by
de Groot and others that have become influential in the understanding of
human perception. Chapter 5, which concerns memory, is more extensive
and includes aspects that have been well researched in other domains, such as
verbal learning. Again, chess dominates the literature; other championship
games enter the stage more emphatically, refining and qualifying the results
obtained with chess. In Chapter 6, the details of problem-solving experiments
are explained. This chapter completes the overview of board games and
cognitive psychology, which has focused on the study of expertise.
   Chapter 7 addresses the notion of time, with a focus on learning, develop-
ment, and ageing. Developmental psychology has also included research on
board games and, again, this research is focused on cognition. The develop-
mental stages of cognition are discussed with the help of research on games;
this time, chess is no longer dominant, but largely replaced by research on
African and Asian games. A related topic is discussed in Chapter 8, where
the principles of education also include ideas on development and cognition.
Here the theories are limited to those directly related to playing board games,
i.e. learning how to play, and using board games in teaching.
   Chapter 9 introduces other disciplines in which board games have enriched
our understanding of the human mind. Data about the psychology of
intelligence, neuropsychology, and the psychology of personality, emotions
and motivation complete the picture of Homo Ludens that the previous
chapters have outlined.
   Chapter 10 provides a discussion of the methodological problems in board-
game research. Board games have been and are still popular in cognitive
psychology. There remain methodological issues to resolve, in particular in
the fields of cross-cultural, developmental, and educational studies where
ideal experiments are rarely practical.
   Finally, a list of references and three appendices complete this systematic
study.
2      Formal analyses of
       board games




The study of board games in computer science and artificial intelligence has
generated a considerable literature, which can only be briefly surveyed here.
Ignoring chess automata—most of them have turned out to be fraudulent—
computer game playing started at the beginning of the twentieth century with
Torres y Quevedo’s chess machine, which was able to play the endgame King
and Rook against King. In his classic 1913 paper, Zermelo formalized the
concept of game tree. Just after World War II, Shannon (1950) augmented
ideas proposed by Turing in the forties (Turing, 1953), and described a com-
puter program able to play an entire game of chess, either by full search to
a specified depth or by selective search. Since Shannon’s seminal paper, com-
puter scientists have developed many techniques for improving the efficiency
and selectivity of search algorithms. Combined with powerful hardware, this
‘brute-force’ approach, as it is often called, has enabled computers to play a
number of board games at world-class level.
   The ideas introduced by Zermelo and Shannon played an essential role not
only in game theory, computer science, and artificial intelligence, but also in
psychology. The goal of this chapter, then, is to give a brief introduction to
key concepts from formal analyses of games. Our interest will be in explain-
ing the conceptual tools used in later chapters, rather than in providing an
extensive discussion of these tools. Thus, our review will be biased toward
issues that are of psychological interest.
   We start with computer science and artificial intelligence, and introduce
the question of search, which has dominated enquiries in these fields. We
then consider the role played by knowledge in computer programs, and the
extent to which these programs learn. The second part of the chapter deals
with various aspects of game complexity, considering features such as tree
complexity and move complexity. We also discuss applications of Shannon’s
information theory to the analysis of board-game complexity.
12   Moves in mind
Fundamental concepts

Game tree
Trees are a popular representation in computer science. In the case of game
trees, the current state or position is represented by a node (the root node)
at the top of the tree. Subsequent positions are represented by nodes below
this node. A branch between two nodes represents a movement of either
opponent. (Computer scientists call the movement of a single opponent a
‘ply’, and reserve the term ‘move’ to characterize a movement of both
opponents; that is, a move consists of two ply.) The nodes at the end of a
sequence of moves are called ‘leaves’, and the nodes between the root node
and the leaves are called ‘internal nodes’. In addition to the total number of
nodes, several measures can be taken from trees, including: depth (distance
between the root node and a leaf), branching factor (the number of branches
below a given node), and summaries of these values (e.g., averages, standard
deviations, maxima). Figure 2.1 illustrates the concept of tree, and Figure 2.2
shows its application with the game of tic-tac-toe. Trees can also be used to
characterize the entire space of a given game or the amount of search carried
out by a computer or a human (see below and Chapter 6).


Game graph
While versatile from a computer-science point of view, search trees have the
shortcoming that the same position may be represented by different nodes
in the tree (e.g., due to transposition of moves). In order to capture this
property, a different representation may be used: graphs. Like trees, graphs
are made of nodes and links. With board games, the links are directed (they
can be taken in only one direction). Instead of showing how variations
originate from a given position—what trees do—graphs show how positions
are interconnected, each position being represented only once. In general,
graphs are used less often than trees in computer games, because they are




Figure 2.1 Illustration of the concept of a tree.
                                             Formal analyses of board games        13




Figure 2.2 A game tree for tic-tac-toe. In this example (after Lindsay & Norman,
           1977), the tree has been kept simple by assuming that the first player chose
           the centre position.




Figure 2.3 Game graph for Figure 2.2.


more costly computationally. Figure 2.3 shows the graph corresponding to
the states depicted in Figure 2.2.


Board games in computer science and artificial intelligence
The study of computer games has evolved into a respectable research field
within computer science and artificial intelligence. An entire journal, the
Journal of the International Computer Games Association, is devoted to
the study of algorithms in computer games. Originally dominated by com-
puter chess, the contributions to this journal now include the whole gamut
of games. More so than in psychology, a large variety of board games are
studied in computer science.
14   Moves in mind
The state of the art: Computers as world champions
For many years, computer programs were considered with amusement by
serious players of many board games, as the accomplishment of these
programs was rather mediocre. This is no longer the case. Progress on
search techniques, evaluation functions, and the management of knowledge
has led to the development of programs beating world champions in
several games. A backgammon demonstration match held in 1980 pro-
vided early evidence demonstrating computers’ potential: Berliner’s (1980)
BKG program defeated the world champion 5–1. As noted by Berliner
himself, his program was quite lucky with the dice. Luck is no longer a
good explanation with today’s leading backgammon program: Tesauro’s
(1992) program has ranked consistently among the best players in the
world.
   Checkers was the first game in which a computer beat a reigning world
champion in an official match. In August 1994, checkers world champion Dr
Marion Tinsley resigned the match and the world champion title to Chinook,
after six draws (Schaeffer, Lake, Lu, & Bryant, 1996). While this victory
was marred by the human champion’s ill health, Chinook’s achievement
is beyond doubt: it defended its title in two subsequent matches, and,
previously, had beaten Tinsley in two games—not a mean feat, given that
Tinsley had lost only five games against human players between 1950 and
1992! Chinook’s parallel hardware and search algorithms allowed it to search
an average minimum depth of 21 ply, not including search extensions (see
below). It also had access to an extensive opening book, and to endgame
databases containing 148 billion positions.
   The culmination of the brute-force approach was the year 1997, when two
world champions were defeated in regular matches in chess and Othello. In
May, Deep Blue beat chess world champion Gary Kasparov 3.5–2.5, realizing
one of the old dreams of artificial intelligence (Campbell, Hoane, & Hsu,
2002). Deep Blue, a typical example of the brute-force approach, owed its
strength mainly to special-purpose hardware, which made it possible to
consider up to 200 million positions per second. It also relied on powerful,
yet efficient, evaluation functions, that were tuned using a combination of
human knowledge and sophisticated automated techniques (Tesauro,
2001). In August, the program Logistello (Buro, 1999) defeated Othello
world champion Takeshi Murakami 6–0. The program combined new
approaches for the construction and combination of evaluation features,
selective search, and learning. It also relied on an automatically updated
opening book, and on fast hardware that allowed it to search about 160,000
nodes per second in middlegames and about 480,000 nodes per second in
endgames.
   In 2002, chess world champion Vladimir Kramnik failed to beat Deep
Fritz, a commercial program, having to content himself with a 3–3 draw. A
similar fate awaited former world champion Gary Kasparov in 2003 against
                                          Formal analyses of board games    15
the program Deep Junior. When one adds to this list games such as awele,
dakon, four-in-a-row, and gomoku, which have been ‘solved’, and where the
computer plays perfectly (see below), one realizes that computers have
conquered most of the board-game territory. The notable exceptions are Go
and shogi.


Elements of computer search
In his seminal paper, Shannon (1950) proposed two types of search. In type-
A search, all moves are investigated to a predefined depth, and the leaf nodes
are evaluated (more about evaluation below). An obvious weakness of this
approach, noted by Shannon himself, is that the evaluation can sometimes be
done in the middle of an exchange or in the presence of a strong threat. Given
that most evaluation functions are simple, these particularities would not
be taken into consideration, with disastrous consequences for the program.
The second type of search, type-B search, addresses this issue. ‘Interesting’
lines—for example, lines containing dynamic threats—are continued until a
quiescent position is reached. Shannon also proposed a type-C search, where
plans are taken into consideration. Little research has been done on this topic
in computer science (see below and Chapter 6).
   Type-A and type-B search use the minimax algorithm, first proposed by
Shannon (1950) and Turing (1953). The program computes the evaluation
of all leaf nodes, and then backs up the information to the root node, by
choosing the moves that minimize the value of the position with the
opponent’s moves and maximize this value with the program’s own moves
(see Figure 2.4). Obviously, looking at all moves to a given depth is time
consuming. For example, in chess, there is an average of 35 moves possible in
each position. Thus, a search 10 ply deep would have to consider 3510 moves.
To cut down the number of positions to consider, several techniques have
been developed. The most commonly used is the alpha-beta algorithm, which
cuts off variations that have no consequence on the outcome of search: if a
move b has already been ‘refuted’ by a variation and shown to be inferior to
another move a previously analysed, there is no need to search additional
variations following b.
   Since the early days of computer games, techniques for improving the
efficiency of search algorithms or to make search more selective have
been extensively studied (see Levy & Newborn, 1991; Newell & Simon, 1972).
For example, the ‘singular-extension’ technique continues searching moves
that return a much higher value than alternative moves. The ‘killer-move’
heuristic keeps a short list of moves that had a dramatic impact in previous
variations, and considers them first in future analysis. A modification of
this heuristic, called the ‘history heuristic’, keeps track of all moves and of
how often they led to a refutation in previous variations, and sorts the list
of possible moves by giving higher priority to moves that led to more
refutations.
16   Moves in mind




Figure 2.4 A very simple example of minimax illustrated with the game of awele. The
           current situation is represented at the top of the figure. In the centre part
           of the figure, all possible moves are considered and evaluated (number
           of seeds captured) for each player. Then (bottom part of the figure) the
           minimax algorithm allows the computation of the best move—1 in this
           case.

Evaluation functions
Given that evaluation functions are used very often, they tend to be simple.
Typically, they consist of a polynomial function combining numerical infor-
mation about material, space, some measure of safety, and development.
                                          Formal analyses of board games     17
While the structure of the search algorithm tends to be the same from
game to game, the content of the evaluation function is specific to a given
game. This content can be seen as an implicit form of knowledge.
   The search techniques that we have briefly described, combined with
sophisticated but efficient evaluation functions, have enabled computers to
reach top level in most board games. Indeed, the field has been dominated by
the questions of search and evaluation, and the question of knowledge has
attracted relatively little attention. The exception is Go, where search trees
turn out to be prohibitively large, with the consequence that even the best Go
programs do not play better than human novices. Go is then a domain where
there is strong pressure to incorporate knowledge to search mechanisms.


Role of knowledge in computer games

Chess
The importance of knowledge in game playing has never been denied, even in
the early days of artificial intelligence, where emphasis was given to search
mechanisms. (This emphasis is partly explained by the limited amount of
computer memory available in the 1950s and 1960s.) However, the impor-
tance of knowledge was especially stressed in the late 1970s and early 1980s—
the period during which expert systems became fashionable in artificial
intelligence. Of particular interest is Berliner’s (1981) paper, in which he
provided a theoretical analysis of the interaction between search and know-
ledge. Noting that knowledge reduces the need for search, he proposes that
knowledge has a ‘property of projection ability’. Thus, tactical knowledge
may replace a 9-ply search for a Pawn win, positional knowledge may replace
a 25-ply search, and strategic knowledge may replace a 45-ply search. Know-
ledge is also critical if one wants to evaluate the leaf nodes efficiently. In
Berliner’s words (1981, p. 11): ‘Knowledge without search has limited utility
as has search without knowledge.’
   Berliner (1981) discusses two ways knowledge impacts on search. First,
knowledge can limit the number of moves to consider, for example, using the
semantics of the position. This ‘knowledge-directed’ search (or best-first
search), to distinguish from brute-force search (or full-width search), is dif-
ficult to obtain and necessitates a large body of directing knowledge. Second,
knowledge is used for evaluation at the leaves of the search tree. This terminal
knowledge must be present both for knowledge-directed and brute-force
search. As noted above, the evaluation function must be efficient, as it will be
used a large number of times during the analysis.
   A natural way to explore knowledge is to study pattern recognition, an
approach that has been used for the development of several programs.
Church and Church (1977) have implemented a program playing speed chess,
which essentially uses goal-directed pattern recognition. The program first
carries out a static analysis of the patterns on the board and determines
18   Moves in mind
what goals are practical. There are different goals for openings, middlegames,
and endgames. In the second stage, the program tries to achieve the most
promising goal; when this is not possible, it uses another goal. CHUNKER
(Berliner & Campbell, 1984) treats a position as small clusters of pieces
(chunks), like human players. These chunks, which are stored in a library,
have properties associated with them. CHUNKER led to the revision of the
(human) judgement of some complex Pawn endgames. Knowledge of patterns
is also discussed by Bratko and Michie (1980), for endgames King + Rook vs.
King and King + Rook vs. King + Knight, and also by Tan (1977), who was
interested in ways to represent Pawn structures.
   Berliner and Ebeling (1989) describe SUPREM (Search Using Pattern
Recognition as the Evaluation Mechanism), a problem-solving architecture
based on a combination of rapid search and pattern recognition. Imple-
mented using the chess machine Hitech, this approach made it possible to
develop a strong program, playing at grandmaster level. Berliner and Ebeling
(1989) emphasize two points. First, the more a process can look ahead,
the less it needs detailed knowledge. Second, it is possible to solve complex
problems with relatively small patterns, if one accepts a loss of generality and
if one uses probable and redundant patterns.
   The amount of information necessary to play an entire chess game at a
high level has led researchers to focus on simple cases, mainly endgames, in
which few pieces are left on the board, such as the endgame King + Rook vs.
King (Michie, 1977) or King + Pawn vs. King (Bramer, 1982; Michie, 1982).
These studies, which were carried out using a representation extending
human patterns, can be contrasted with approaches using databases based on
retrograde analysis (see below).


Go
We have mentioned earlier that traditional search techniques do not work
with Go. Burmeister (2000) mentions two reasons why this is the case. First,
Go researchers do not have adequate evaluation functions allowing the large
search trees to be pruned. Second, the size of the game tree is much larger
in Go than in other board games such as chess; a 19×19 Go board contains
361 points, as compared to 64 squares on a chessboard. Consequently, the
average branching factor is much higher in Go than in chess (on average,
about 200 against about 35), and the size of the state-space (i.e., the number
of possible positions) is also much larger in Go (see below). In addition,
Go games are longer (on average, about 275 ply, as compared to about 80 for
chess).
   Due to these limits, it is not surprising that researchers have tried more
knowledge-oriented approaches. According to Burmeister (2000), the first
fully implemented Go program was developed by Zobrist (1970). Several
important ideas were introduced in this work, including the use of a numeric
influence function to partition the board into black and white territories (see
                                          Formal analyses of board games     19
Figure 2.5). The influence function was not always reliable, and had to be
supplemented with other information provided by pattern recognition.
   In Zobrist’s program, patterns corresponded to numeric configurations
contained in the program’s memory. Associated with each pattern was a
move, as well as a numeric value indicating the priority of the move. Before
choosing a move, the program attempted to recognize patterns over the entire
board. When a pattern was matched, the associated move saw its numeric
value incremented by the priority of the move. Once the entire board had
been searched for patterns, the move with the highest value would be selected.
   Another line of research attempted to develop a Go program based around
human perception and planning (Reitman, Kerwin, Nado, Reitman, &
Wilcox, 1974; Reitman, Nado, & Wilcox, 1978; Reitman & Wilcox, 1978,
1979; Wilcox, 1988). In order to understand these abilities better, the
researchers videotaped protocols and post-game analyses of a strong Go
player. Based on these data, they proposed three key ingredients to a Go
program: perception, knowledge, and coordination. Knowledge is further
divided into process knowledge (e.g., how to make territory), and evaluation
knowledge (e.g., judgement of the stability of groups).
   The control structures of Reitman and Wilcox’s program enabled co-
ordination of perception and knowledge. Specifically, the program main-
tained a representation implemented as a multilevel network. A hierarchy of
experts and critics operated on this network, which was selectively updated.
In particular, search was selective, goal driven, and local (rather than carried
out on the whole board). The program was estimated to have a strength of
27 kyu (Reitman & Wilcox, 1978), and had a style that looked rather human,
preferring defence over attack, and having difficulties when several groups
were put under pressure at the same time.
   Current Go programs use a variety of approaches to handle domain-
specific knowledge. A good example is offered by Fotland’s program, called
‘The many faces of Go’. We limit ourselves to a brief description, and refer




Figure 2.5 Zobrist’s (1970) influence function, which computes a numerical value
           for every point on the board. The figure shows the pattern of influence
           radiating from a single black stone. (After Burmeister, 2000.)
20   Moves in mind
the reader to Burmeister (2000) for an extensive discussion. The program
stores a position in three classes of dynamic data structures (incremental,
locally recalculated, and globally recalculated). These data structures encode
Go-specific knowledge, such as ‘strings’, ‘eyes’, and ‘territory’. Local search,
which normally does not exceed 12 ply, is carried out by a ‘tactician’ module.
   Like Zobrist’s program, Fotland’s program employs an influence function.
It also uses a database of patterns (about 1,200 patterns of size 8 × 8), where
each pattern is associated with a move tree (on average five moves deep). The
program has a database of ‘joseki’ (standard sequences of moves near the
corner of the board), containing about 45,000 moves, organized in a single
graph. Generating a move involves four steps: first, strategic evaluation and
selection of goals; second, generation of candidate moves with full board
look-ahead; third, move evaluation, either using evaluation of the full
board or using the strategic goals; and, finally, selection of the best move.
From this brief description, it clearly appears that Fotland’s program has a
rich knowledge base, where information about stone location is closely linked
to information about search.


Computer databases and retrograde analysis
Brute-force search starts looking ahead from a given position, and then
explores the tree of possible moves. Another application of brute force,
called retrograde analysis, is to do the opposite: to start from all possible final
positions in a game (e.g., in chess: checkmate, stalemate, draw due to a lack
of material). All these positions are evaluated as win for white, win for black,
or draw. Then, the program generates all parent positions that lead to one
of these final positions. These parent positions will inherit the value (win or
draw) of the final position to which they lead. In the next step, the grand-
parent positions are generated and evaluated. Then, one simply applies the
method recursively, until all legal positions in a game have been directly or
indirectly linked to a final position. Once the entire game tree is catalogued
using this method, the game has been solved: one knows if there is a winner
with optimal play, and, if so, who is the winner. Obviously, the size of the
game tree is a critical factor for the application of this technique. Even with
relatively simple games (e.g., nine-men’s morris), it generates a large number
of positions, which have to be managed using sophisticated database
techniques. For any nontrivial game, one needs a massive amount of com-
putation, and for games with a large problem space like checkers, chess, or
Go, only subsets of the game have been solved this way.
   The idea of retrograde analysis is old, going back at least to Zermelo
(1913). But it is only with the advent of powerful computers that its applica-
tion was made possible. The method was first applied in the 1970s with simple
chess endgames (e.g., Clarke, 1977; Thomson, 1986). Since then, retrograde
analysis, often supplemented by other techniques, has led to the solution of a
number of board games (van den Herik, Uiterwijk, & van Rijswijck, 2002),
                                          Formal analyses of board games    21
including nine-men’s morris (also known as mill; Gasser, 1990, 1995),
gomoku (Allis, 1994), awele (Romein & Bal, 2002), and kalah (Irving, Donk-
ers, & Uiterwijk, 2000). In chess, all endgames of up to five pieces have been
solved, and databases have been created for some endgames with six pieces
(Levy & Newborn, 1991; Thomson, 1996). For checkers, Chinook contains
all endgame positions of seven pieces and less, and all endgame positions of
four pieces against four (Schaeffer et al., 1996).
   A frequent remark in the psychological literature on problem solving in
board games (Chapter 6) is that it is difficult to analyse the solutions pro-
posed by humans because, in most cases, one does not know what is the best
move. In this respect, retrograde analysis is of interest to psychologists,
because the complete analysis of games or endgames gives knowledge of
perfect play, and thus enables experiments where the task environment is
entirely controlled. For example, Jansen (1990, 1992) had participants play
the King + Queen vs. King + Rook endgame against a database, which
enabled him to extract a number of heuristics commonly used by humans.
Interestingly, some of these heuristics led to poor moves as compared to
optimal play, although they facilitated human search by directing it to
positions with a low branching factor. Another application of databases is
to compare the actual play of masters with optimal play (e.g., Jansen, 1990,
1992; Nunn, 1994). A final application is to use perfect play to extract
heuristics useful to humans. So far, this has turned out to be difficult in games
such as chess, partly because many moves resist classification under simple
heuristics, but it has been accomplished for mathematically less complex
games such as connect-four (Allis, 1988).


Machine learning
Machine learning in board games started with Arthur Samuel’s (1959)
checkers program, which demonstrated that simple but powerful mechanisms
could lead to substantial learning in a difficult game. His program improved
by using a number of techniques, including tuning its polynomial evaluation
function and remembering the outcomes of endgames. Unfortunately, this
early success was not followed up (probably due to limits in hardware
capacity), and there was no resurgence of interest in artificial learning until
the 1980s. Recently, there has been considerable work in the application of
machine-learning techniques to games in general and board games in par-
ticular (Fürnkranz & Kubat, 2001). More generally, machine learning is
now an important subfield of research in artificial intelligence. A number of
techniques have been applied to board games, some with remarkable success.
For example, Tesauro (1995, 2002) developed a backgammon program based
on a combination of neural-net and temporal-difference learning. Temporal-
difference learning is a technique, introduced by Samuel (1959) in his
checkers program and later refined by Sutton (1988), for estimating the long-
term cost of a choice as a function of the current state. Tesauro’s program,
22   Moves in mind
which learns exclusively by playing against itself, reached world-champion
level.
   In this section, we will limit ourselves to highlighting some interesting
work from a psychological point of view, and refer the reader to Fürnkranz’s
(2001) review for detail.


Chess
Machine-learning techniques in chess can be classified as symbolic (e.g.,
methods based on first-order logic), nonsymbolic (mainly neural-net
approaches), and statistical. Most research has been carried out in the first
category.
   Baxter, Tridgell, and Weaver (1998, 2001) employed temporal-difference
learning to tune the parameters of the evaluation function of their program,
which otherwise uses standard search techniques. The program, called Knight-
Cap, was trained by playing on an Internet chess server. After about 1000
games, its rating had increased from 1600 Elo (average amateur) to 2150 Elo
(strong Expert). Fürnkranz (2001) notes that an important ingredient to
KnightCap’s success was a combination of variety and constancy in
opposition strength: it played against human opponents of varying strengths,
but it also tended to play more often against players of the same strength.
   A number of programs acquire chess patterns. We will consider CHREST
and CHUMP in detail later in this book, and discuss other attempts here.
TAL (Flinter & Keane, 1995) acquires abstract patterns from a selection of
games played by former world champion Mikhail Tal. Using the approach
of case-based reasoning, it attempts to decompose the position into simpler
components. CASTLE (Krulwich, 1993) uses the technique of case-based
planning (Hammond, 1989). In this technique, plans generalized from past
experiences are reused; when they fail, they are ‘debugged’. CASTLE was
able to learn plans for short-term threats such as forks, pins, and discovered
attacks.
   MORPH (Levinson & Snyder, 1991) uses pattern-weight pairs, where
patterns are graphs representing pieces and their relationships. Patterns are
coupled so that they can produce evaluations. A variant of temporal-
difference learning is used to adjust the weights of the patterns. MORPH
plays by pure pattern recognition (i.e., it does not carry out any search), by
selecting the move proposed by those matched patterns having the highest
value. In the same line of research, Finkelstein and Markovitch (1998)
developed a program in which patterns are associated with moves. The
program learns to refine both patterns and sequences of moves, which allows
for a highly selective search.
   Pitrat’s program (1976a, 1976b) learns definitions of simple chess concepts
such as pin or fork. The program uses move trees as basic representations.
These move trees are simplified as a function of learning, with unnecessary
moves deleted and important moves generalized, the exact location of a piece
                                          Formal analyses of board games     23
being replaced by a variable. While the program was able to learn a number of
useful patterns, it was hampered by the fact that the move trees tended to
grow too large after some knowledge had been acquired.
  Researchers have also used neural-net techniques. For example, both Thrun
(1995) and Tesauro (2001) used a neural network to tune the weights of the
evaluation function. The final approach is to use statistical techniques on large
databases of games in order to identify principles and regularities about vari-
ous aspects of the game, in particular endgames. Here, unlike the two previous
approaches, the goal is not to produce playing programs, but to improve our
understanding of a given game (e.g., for chess, Sturman, 1996). This com-
plements work on endgames using retrograde analysis (see above), and also
raises interesting psychological questions as to why humans were able to learn
some of these principles (e.g., strength of Bishop pairs in open positions), but
not some others (e.g., that the advantage of Queen and Knight over Queen
and Bishop vanishes when additional pieces are present (Sturman, 1996) ).


Go
Both symbolic and nonsymbolic learning techniques have been used in Go.
Gogol (Cazenave, 1996a, 1996b) is a rule-based program where Go know-
ledge is represented by a formalism mixing first-order logic and a variation of
‘combinatorial game theory’. (Combinatorial game theory is a mathematical
method where games are analysed in terms of smaller and independent
subgames.) The several thousand rules used by Gogol are implemented as
pairs comprising premises and conclusions. A deductive learning algorithm is
used to learn new rules.
   Several Go programs learn by using neural-net algorithms, with varying
pre-coded knowledge. At one extreme, one finds Gobble (Brügmann, 1993),
which does not have Go knowledge beyond the rules. Gobble learns with
‘simulated annealing’, a technique inspired by the process of progressively
lowering the temperature of a melting substance until it solidifies. At the
other extreme, there are programs like NeuroGoII (Enzenberger, 1996),
which uses expert Go knowledge. This knowledge is combined with learning
methods based on a combination of back-propagation and temporal-
difference algorithms.


Other games
Learning techniques have been used in a variety of other board games,
including Othello, tic-tac-toe, and checkers (for a review, see Fürnkranz,
2001, as well as the chapters contained in Fürnkranz & Kubat, 2001). For
psychologists interested in both learning and board games, a most interesting
program is HOYLE (Epstein, 2001; Epstein, Gelfand & Twersky-Lock,
1998), which specializes in learning and playing simple board games. The
games tackled are all two-person, perfect-information games, and include
24   Moves in mind
games such as tic-tac-toe and nine-men’s morris. HOYLE begins at novice
level and then improves by playing. Several hierarchically organized
‘advisors’ vote on the quality of the potential moves. These advisors are
originally domain independent and coded by the programmers, but, as the
program becomes better in a given game, they automatically acquire game-
specific weights as well as spatially oriented patterns and heuristics. These
patterns and heuristics use visual features that are naturally perceived by
human players and that typically follow Gestalt principles: straight lines, Ls,
triangles, squares, and diagonals. The program also learns from mistakes.
After each decisive game, it identifies the last position in which the loser has
an alternative move; through exhaustive search, it attempts to estimate the
value of this position. The result of the search is then saved for future games.

Opponent modelling
Theory of mind is currently a fashionable topic in psychology: how do
humans, and perhaps other species, represent the thoughts of other indi-
viduals? In the framework of games, the question is to understand how
players model their opponent—how they anticipate and understand his or
her actions. The necessity of such modelling obviously varies from game
to game, with games such as poker being at one extreme and games such
as tic-tac-toe at the other. In pioneering work, Jansen (1990, 1992, 1993)
investigated how a computer could take advantage of its knowledge of a
fallible opponent to improve its performance over rational play obtained,
for example, by minimax search. Various statistics collected about search
behaviour enable the extraction of metaknowledge about characteristics
of the opponent’s algorithm. In particular, knowledge of specific search
characteristics, including limited depth of search, suggests the creation of
‘swindle’ positions, that is, positions in which the search algorithm used by
the opponent leads to an incorrect evaluation. These theoretical speculations
led Jansen to carry out experimental research, where humans faced a com-
puter sometimes choosing suboptimal moves (from a game-theoretic point of
view) in the hope that it can ‘swindle’ the opponent.
   Donkers, Uiterwijk, and van den Herik (2001, 2002, 2003) have developed
a probabilistic version of opponent-model search, which models multiple
opponents, and consequently faces uncertainty about which model of the
opponent is the correct one. Using both theoretical and empirical investi-
gations, they are trying to specify the conditions under which classical and
probabilistic opponent-model search can improve over minimax search. For
example, what are the consequences of the risks incurred by modelling
the opponent, such as imperfect knowledge of the opponent and low-level
quality of the evaluation function? Donkers and colleagues are also inter-
ested in developing algorithms efficient in realistic settings (such as four-piece
chess endgames or Soucie’s board game of ‘lines-of-action’), and in develop-
ing techniques for automatically learning an opponent’s model.
                                          Formal analyses of board games    25
   Two other machine-learning projects have produced programs auto-
matically building a model of the opponent, based on its moves. Carmel and
Markovitch (1993) developed a checkers program that estimates the depth
of the opponent’s minimax search, and uses this information to model
the opponent. Walczak and Dankel (1993) started from the hypothesis that
human players prefer positions that are simple from a cognitive point of
view—that is, positions that can be expressed using few chunks. Their pro-
gram models the chunks of the opponent; using chunks that are nearly com-
pleted, it predicts the opponent’s next move by assuming that it will complete
them. In chess, the program predicts about 10% of the moves played by
Botvinnik, Karpov, and Kasparov. It has also been applied to Go.
   Thagard (1992) has explored opponent modelling (which he calls
‘adversarial problem solving’) in a wider context. He described the cognitive
mechanisms required to use a mental model of the opponent in decision
making and proposed a connectionist model simulating some military
situations.


Philosophical implications
Board games (in particular checkers and chess) have played an important
role in the philosophical discussion over the possibility of artificial intelli-
gence (what computers can do, and what they cannot do). For researchers
in artificial intelligence, computers have demonstrated that intelligence is
not the monopoly of humans, or even of living creatures. This position was
perhaps best epitomized in Simon and Newell’s (1958) prediction that a
computer would beat the world chess champion within 10 years. At the other
extreme, we find philosophers such as Dreyfus (1972), who argued that
symbolic artificial intelligence, the kind championed by Newell and Simon,
cannot produce true intelligence, because it misses important characteristics
such as having a body and being able to show intuition. While Deep Blue’s
victory over Kasparov in 1997 may have proved both sides wrong—Dreyfus,
because he had principled objections against the possibility that computers
will ever beat a world champion, and Newell and Simon, because their pre-
diction was overoptimistic by 30 years—board games still are a favourite
topic in the philosophical discussion aiming at settling the question of
artificial intelligence (e.g., Gobet, 1997b). As for the question of human
intuition, it will be taken up in Chapter 6.


Information and complexity analysis

Information analysis of games
Information theory, which comes from engineering (Shannon, 1951;
Shannon & Weawer, 1949), is a mathematical theory aimed at measuring
26   Moves in mind
information in precise terms. The amount of information, or incertitude, is
measured as ‘bits’, that is, binary decisions. In the 1960s, de Groot and
Jongman used this approach to better understand the difficulty of the task
facing a chessplayer attempting to memorize a position (de Groot, 1966;
de Groot & Gobet, 1996; Jongman, 1968). They estimated the amount of
information in a legal, but possibly random chess position, as 143 bits. This
is an overestimate, as many of these positions do not occur in ‘reasonable’
games. Combining methods from information theory with a number of
statistical and experimental techniques, they estimated the size of the space
of all positions likely to occur in master games, which allowed them to derive
the information contained in the positions they used in recall experiments.
They obtained an upper limit of 50 bits, and concluded that this number is
‘nothing special’, assuming an efficient coding system—a system that may
require several years of practice and study to acquire. Chase and Simon’s
(1973a) chunking theory, which we will discuss in detail in this book, offers
such a coding system.


Complexity analysis of games
Two types of complexity characterize board games. Computational complex-
ity is based on the size of the problem space in a given game, and includes
measures such as state-space complexity (the number of different positions),
game-tree complexity (the number of leaf positions that can be generated by
search—the same position may be counted several times), average branching
factor, and average game length (see Table 2.1, based on Allis, 1994, and van
den Herik et al., 2002). For example, a comparison of bao with chess from a
computational point of view shows that chess is more complicated.
   Mutational complexity (introduced by de Voogt, 1995, for bao) is expressed
in terms of changes on the board and number of pieces involved in a move.
It is not particularly relevant for computer-playing programs—computer
programs can handle an indefinite mutational complexity—but is critical for
human players. A comparison between Go, gomoku, chess, Othello, awele
and bao shows that the ranking of these games with mutational complexity is
almost the reverse of their ranking with computational complexity.
   In Table 2.1, branching factors and game lengths are estimates. The
maximum number of position changes and pieces involved are theoretical
maxima and do not commonly occur in the game. The game of pegity as
described by Rayner (1958a, 1958b) is not included in the table and has an
identical mutational complexity to gomoku but a higher computational
complexity, since it is played on a 24×24 grid instead of 19×19.
   Townshend (1986, p. 134) provides additional information about
mutational complexity in a table with ‘comparative results of simulated
moves for various capture modes’ in mancala games. This table shows a
number of statistics depicting mancala games with various capture modes.
Townshend concludes that bao features by far the lowest quantity of
                                           Formal analyses of board games      27
Table 2.1 Computational and mutational complexity of selected board games

                                  Go      Gomoku Chess Othello Awele Bao

Computational complexity
State-space complexity            10172   10105    1043    1028   1012        1025
Game-tree complexity              10360   1070     10123   1058   1032        1034
Average branching factor          250     210      35      10      3.5         4
Average game length (ply)         150     30       80      58     60          57

Mutational complexity
Average no. position changes
  per move                        1       1        2        4      4           6
Minimum number of changes         1       1        2        2      2           3
Maximum number of changes         1       1        4       20     12          24

Average no. position changes
  per move including multiple
  changes in position             1       1        2        4      4           8
Maximum number of changes         1       1        4       20     47        >100

Average no. pieces involved in
  move                            1       1        1.5      4      3           6
Minimum number of pieces          1       1        1        2      1           2
Maximum number of pieces          1       1        2       20     48          64


captured counters per take and the lowest turnover per move of counters
between players. In addition, bao achieves by far the highest number of
captures per move, the greatest preponderance of counters on the inner row
(captures are only made on the inner row), and the most counters per hole on
the inner row.


Game theory and the concept of error
In spite of its name, game theory (von Neumann & Morgenstern, 1944) is
more about decision making in situations where there is interest conflict than
about games. While some of its outcomes do obviously apply to board games
(most notably, the minimax principle), they mostly apply to wider domains,
such as economics, politics, and even evolutionary biology.
  From a game-theoretic point of view, most of the games we will discuss in
this book are mathematically trivial: there are two-person, zero-sum games
of perfect information. In other words, whatever one player loses is won by
the other player, and every player knows the results of all previous moves.
Therefore, any of their positions is won, lost, or drawn. There is an obvious
28   Moves in mind
rational strategy to find the value of a given position: generate every branch
in the game tree until a win, loss, or draw position is reached, and assign a
numeric value to each of these final positions (say, 1 for a win, 0 for a draw,
and −1 for a loss); then, propagate this information back to the present
position, using the minimax principle we have described above. In this
framework, the term ‘error’ means a move that has shifted the game-theoretic
value of a position to a lesser value (i.e., from won to drawn or lost, or from
drawn to lost).
   Obviously, this conception of error is different to what is meant by board-
game players. To address this, Simon (1974) developed a mathematical model
for explaining the notion of a ‘losing move’, as the term is used by chess-
players and commentators. In his model, each player has only two moves
available; one increases the value of the position by 1, and the other decreases
it by 1. He used the formalism of a ‘lattice’ (i.e., a set on which a partial
ordering is defined, and that can be represented as a regular arrangement of
points—see Figure 2.6). In the lattice used by Simon, each position has a
numerical value (positive if it favours white, negative if it favours black, and
0 if it is equal). The starting position (assumed to have the value 0) is at the
bottom of the lattice, and terminal positions (lost, drawn, or won) are at the
top. When both players play optimally, their moves can be represented by a
vertical, zigzag path. Weak moves indicate that one player diverges from this
vertical path. Simon assumed that in a game like chess, weak moves do not
necessarily lose the game: the drawing zone is large enough to allow a few
minor errors, or even larger errors if these are counterbalanced by errors
made by the other side. Simon discussed a number of phenomena in the light
of this model, including the effect of limited thinking time, the presence of
‘problematic’ positions (i.e., positions where the move to play is not obvious),
and the play between players of different levels. For example, in the latter
case, the stronger player only has to make ‘standard’ moves to win the
game, waiting for either the accumulation of small errors or the presence of
a blunder to push the opponent to the subset of the lattice where loss is
irremediable. While Simon used the model with chess as an example, it is clear
that it applies to other (board) games as well.


Conclusion
Perhaps, the most important finding from the construction of programs
playing board games using only approximate evaluation functions is that it
takes a huge amount of forward search to match the human selectivity based
on pattern recognition (Gobet & Simon, 2001). Only extremely rapid com-
puters with large memories can perform at the same level as the human top
players. All programs having beaten a world champion—Chinook in checkers
(Schaeffer, Culberson, Treloar, Knight, Lu, & Szafron, 1992; Schaeffer et al.,
1996), Deep Blue in chess (Campbell et al., 2002), and Logistello in Othello
(Buro, 1999)—carried out substantial forward search. In addition, these
                                              Formal analyses of board games   29




Figure 2.6 Lattice for an idealized game. (See text. After Simon, 1974.)


programs also had access to considerable game-specific knowledge, both
about human experience, as crystallized by thousands of lines of opening play,
and about computer-generated strategies for playing endgames. Learning
techniques were also often used to optimize the parameters of the evaluation
function (e.g., with Deep Blue in chess, see Tesauro, 2001). Hence, it is not
quite true to claim that Deep Blue, Chinook, or Logistello operated solely by
brute force. All supplemented their superior computing powers with extensive
game-specific knowledge.
   Theoretical analyses of board games, such as those offered by information
theory and complexity theory, are important to psychologists, because they
enable a better understanding of the task environment. The quantification
they provide also suggests new experimental approaches to study the means
used by human beings to face the complexity of the task. This was illustrated
by de Groot and Jongman’s research in the 1960s. Ultimately, a better under-
standing of the task environment and its complexity will allow researchers to
develop better cognitive theories of board-game behaviour. This theme will
accompany us in almost all chapters of this book.
   While influential in the development of computer science and artificial
intelligence themselves—think of the impact of concepts such as search
tree and temporal-difference learning—tools and concepts developed for
producing computers playing a strong game have also had important reper-
cussions for psychology. For example, Holding (1985) has proposed that
computer algorithms could offer a model of how humans select a move in
chess (see Chapter 6). Similarly, Ratterman and Epstein (1995) have proposed
30   Moves in mind
that the HOYLE program could be used as a cognitive model of board-game
playing.
   There is no doubt that the central question surrounding board games in
computer science and artificial intelligence—the trade-off between search
and knowledge—has also dominated research in psychology. We have seen in
this chapter that computer science and artificial intelligence have provided
one solution—as we shall see, humans have provided a different one. For
many games, it is clear that artificial means produce better play than human
methods; for others, humans still hold, although it is almost certain that they
will succumb to the precision of artificial means. In both cases, artificial
methods, while using a substantial amount of knowledge, rely mainly on
brute force; the highly selective search shown by humans is still far from being
equalled by machines. For the time being, the challenge faced by artificial
intelligence is mainly posed by games such as Go, where nonselective search
has clearly failed so far. Current programs based on knowledge do not fare
that well either, and this is perhaps one field of research where results from
psychology may have a direct impact.
   More so than research into search algorithms and evaluation functions,
it is research into machine learning and opponent modelling that offers
the highest hopes of cross-fertilization between artificial intelligence and
psychology. Topics like planning, pattern recognition, and, of course,
learning were addressed in these studies, topics that are all crucial for an
understanding of human decision making. Some of the models can be used
directly to derive specific hypotheses about human cognition and investigate
questions about human learning and errors, as compared to machine learning
and errors (e.g., Ratterman & Epstein, 1995).
   Finally, several ideas, such as selective search, progressive deepening,
and pattern recognition, were directly imported from research in human
psychology into computer science. These ideas have benefited artificial-
intelligence research on game playing, even though this research is motivated
by the aim of producing strong programs, whether they play in a human
manner or not.
3      Theories of board-game
       psychology




The goal of this chapter is to provide an overview of the theories that have been
developed to understand how people play board games. The presentation,
which follows a roughly chronological order, only considers theories pub-
lished in the psychological literature. We first focus attention on theories that
have a broad aim but were developed mainly to explain phenomena related
to board games, before we briefly review general psychological theories that
have occasionally been used in the field. As is appropriate for such a topic,
we apply de Groot’s (1946) concept of ‘progressive deepening’: after giving a
summary of the main approaches, we delve into each of them in more detail.


Brief history of board-game psychology
This section gives a historical overview of the key personalities in board-
game psychology, and introduces the main theoretical questions that will
occupy us in most of this book. We first consider chess, which has received
most attention, and then deal with other board games.


Research into expertise in chess
Scientific research into board-game psychology started in Paris with Binet
(1894) and his studies on blindfold chess. Soon after, Cleveland (1907)
published an article that, although it had weak empirical foundations, antici-
pated many of the central topics of board-game psychology, such as the role
of knowledge and the nature of its acquisition. There followed two studies
that emphasized the role of specialized knowledge, as opposed to general
cognitive abilities. The Russian psychologists Djakow, Petrowski, and Rudik
(1927) administered a series of psychometric tests to the best players of the
time, and found differences only when the task was related to chess. In the
Netherlands, de Groot (1946) studied some of the best players of the time,
including world champions Alexander Alekhine and Max Euwe. He used
only chess-related tasks, but essentially reached the same conclusion: chess
skill is domain specific. De Groot also showed that chessplayers are highly
selective in their search.
32   Moves in mind
   De Groot’s research dovetailed with Herbert Simon’s concurrent work
on decision making in organizations, which would later earn him a Nobel
Prize in economics. In particular, Simon was convinced that humans,
contrary to the assumptions of classical economics, cannot aim at optimal
decisions, but are content with ‘good-enough’ solutions. Simon later applied
this idea of ‘bounded rationality’ to other domains, including chess. With
colleagues at the Carnegie Tech in Pittsburgh, he developed computer pro-
grams simulating humans’ selective search (e.g., Newell, Shaw, & Simon,
1958b; Newell & Simon, 1972). He also carried out a programme of experi-
mental and theoretical research (again including computer simulations),
aimed at unravelling the perceptual and memory mechanisms of chess
experts (Simon & Chase, 1973). This led to the formulation of the ‘chunking
theory’, which, as will be made clear in the remainder of this book, has
had a strong impact on research into the psychology of board games
and beyond.
   At about the same time, Tikhomirov and his colleagues at the University
of Moscow were carrying out a series of chess experiments on cognition,
motivation, and emotions. The theories developed by the Russian group
are holistic, and cognition is seen as the dynamic interplay of Gestalts modu-
lated by motivational factors. This is in clear contrast with most research in
Western board-game psychology, which has been essentially analytic.
   The 1980s and 1990s saw the emergence of several theories, some of
them heavily influenced by the chunking theory. Holding’s (1985) theory
emphasizes the role of search and knowledge and suggests that human
experts search in ways similar to computers. It was developed as an
alternative to the chunking theory, which was strongly criticized in Holding’s
book. Saariluoma’s (1984, 1995) apperception-restructuring theory pro-
poses that players, while thinking about a position, use perceptual chunks
to access goal positions by ‘apperception’—that is, by conceptual per-
ception. Gobet and Simon’s (1996c, 2000a) template theory, a direct out-
growth of the chunking theory embodied as a computational model, aims to
account for the findings inconsistent with the original theory, while keeping
its strengths.


Research into other board games
As far as we know, and disappointingly, no independent theoretical work
has originated from research into other board games. In this case, three
main theoretical approaches may be identified. First, research has tested
various aspects of the chunking theory. Second, concepts from cross-cultural
psychology have been of relevance to African games, such as awele and bao
(Retschitzki, 1989, 1990; de Voogt, 1995, 2003). Finally, other studies have
used general theories of psychology, which we consider now.
                                       Theories of board-game psychology     33
Other theoretical influences
While the theories briefly reviewed above cover a substantial portion of the
board-game literature, they by no means account for all theoretical ideas used
in this field. A number of other concepts and mechanisms were imported
from frameworks developed in other areas of psychology. These can be
classified into three areas: frameworks spanning a number of psychological
disciplines (e.g., connectionism or theories emphasizing the role of the
environment); broad theories developed within one branch of psychology
(e.g., Piaget’s theory of development or Freud’s theory of psychoanalysis);
and theories developed in cognitive psychology (e.g., various theories of
intelligence and talent, including Chase & Ericsson’s (1982) skilled-memory
theory). Finally, a number of studies were atheoretical, limiting themselves to
a description of the behaviour observed.
   After this overview of board-game psychology, we are in a position to
discuss each approach in detail. We start with theories originally aimed at
explaining expert behaviour in chess.


Theories of chess skill

Binet’s studies of blindfold chess
In the first empirical study to deal with the psychology of chess—and of any
board game for that matter—Binet (1894, 1966) addressed the question of
visual images in blindfold chess. In this variant of the game, a master plays
one or several games without seeing the board. To collect information about
the cognitive mechanisms underlying this feat, Binet sent a questionnaire to
some of the best players in Europe. While his working hypothesis was that
players had a concrete and detailed representation of the board, their answers
led him to conclude exactly the opposite: in blindfold chess, players’ represen-
tations are abstract and do not encode the detail of the board and the pieces.
Binet believed that his study had highlighted three essential features of
chess psychology. First, personal study and practical experience leads to the
acquisition of domain-specific knowledge, which Binet called ‘erudition’.
This schematic knowledge allows players to integrate moves into a meaning-
ful context. Second, there is ‘imagination’, i.e., the ability to visualize a
position. As mentioned, Binet found that players do not use a detailed visual
memory, but abstract the important features of the position. What remains
at the concrete level are squares with fuzzy boundaries and pieces with
imprecise shapes and colours. Third, there is ‘memory’, which includes visual
memory, touch memory, and verbal memory. In particular, verbal memory is
important for blindfold chess; it allows one to reason about the game, and to
anticipate moves, to reconstruct imagined positions by reminding oneself of
the moves played—which, in blindfold chess, are said out loud—and finally
to identify the colour of squares by using mnemonics.
34   Moves in mind
   Recent research supports Binet’s conclusion that knowledge, and not
visualization, is the essential ingredient of chess skill (see Chapter 5). Even so,
Binet’s method (use of questionnaires) appears weak, as it is now known that
retrospective protocols are not reliable unless corroborated by other means,
and his theoretical explanations are not convincing. In particular, they
include, in the same logical framework, entities that are different at the psy-
chological level (Gobet, 1993b; de Groot, 1946). To be fair with Binet, such
theoretical weaknesses are typical of the state of psychology at that time.


Cleveland and the development of skill
Like Binet, Cleveland (1907) was interested in the role of mental imagery in
chess. While his methodology—questionnaire and introspection—is weak by
current standards, some of his results remain of interest. Cleveland pro-
posed that players could be split into three categories: players who concretely
visualize the board, players who concurrently use a verbal and pictorial
representation, and, finally, players who do not use any visual images at all.
However, the real interest of Cleveland’s paper is not in his treatment of
visual imagery, but in his speculations about the nature of skill.
   Cleveland stressed that the abilities characteristic of chess skill—domain-
specific memory, perceptual speed, and constructive imagination—are
limited to chess and do not correlate with general intellectual abilities.
Cleveland also suggested that players search only a few moves ahead
(between four and six), and that the depth of search depends on whether
the position is tactical or strategic; he also proposed that the moves of the
opponent are harder to anticipate than one’s own. During openings and
endgames, players use a type of reasoning similar to categorical syllogism in
logic. However, the complexity of middlegame positions means that players
cannot use such a clear-cut mode of thinking. In this case, they rely more on
recognizing key aspects of positions. When they cannot rely on experience,
they fall back on trial-and-error methods.
   Cleveland speculated about the development of chess skill. According to
him, players move through five stages, the boundaries of which are arbitrary,
starting with the beginner stage where the name and moves of the pieces are
learnt, and ending with the final stage where ‘positional sense’ is acquired and
tuned. This sense, developed through long experience with the game and
characterized by the application of principles, makes it possible for players to
limit their search to the essential characteristics of the position. Cleveland
also addressed the learning mechanisms underlying these stages. He proposed
that knowledge progressively becomes organized in a hierarchical fashion,
which reflects expanded methods of generalization, increased symbolism,
and an increase in the number of mental associations possible. Thanks to
this organization, players can attend to increasingly larger and meaningful
units, abstract details away, develop mental shortcuts, and memorize new
concepts rapidly.
                                       Theories of board-game psychology      35
   While Cleveland’s description was vague in places and not buttressed by
any experimental data, it captured some of the concepts that were later
developed to explain expert behaviour in cognitive terms. It is therefore
surprising that Cleveland’s paper had been almost forgotten for about 80
years, until it was brought back to attention through Holding’s work
(e.g., Holding, 1985).


Djakow, Petrowski, and Rudik: In search of mental abilities
Taking advantage of the 1925 Moscow tournament, which gathered some
of the best players of the time, Djakow et al. (1927) carried out a series
of psychological experiments with chess masters and non-players. Chess
masters performed better than the control group in tasks related to chess,
such as the memory for dots in an 8 × 8 matrix presented for one minute or
the memory for a position (see Figure 3.1). (Djakow et al. used an artistic
chess problem, where white has to mate in n moves. Chess problems do
not resemble positions normally met in chess games.) With other tasks, no
difference was found. At the end of their book, Djakow et al. list 16 physical
and mental qualities thought to describe chess masters’ mental apparatus.
While the validity of this list is dubious, it had some impact in the sense
that proponents of chess education often use it to highlight the benefits of
chessplaying. Indeed, this list is odd, because it contains domain-free abilities




Figure 3.1 Position used by Djakow, Petrowski and Rudik (1927) in their memory
           task.
36   Moves in mind
(such as ‘objectivity and realism’ and ‘self-confidence’), while, in fact,
the results of Djakow et al. show that expertise in chess is limited to its
domain.
   The work of Djakow et al. has influenced further research through the
chess recall task, which has been extensively used in the last decades. An
important link between the Russian group and current research was provided
by Adriaan de Groot.


De Groot: Selective search and perceptual knowledge
De Groot’s research is discussed at length in Thought and Choice in Chess
(1946, 1965, 1978); shorter accounts may be found in de Groot (1981),
de Groot and Gobet (1996), and Gobet (1999b). His main theoretical
motivation was to apply Otto Selz’s (1922) framework of productive thinking
to problem solving in chess. According to Selz, thinking can be viewed as a
continuous and linear chain of operations. De Groot’s research established
that Selz’s framework could explain the main aspects of chess thinking,
assuming a few extensions and modifications.
  De Groot used only two experimental tasks: a problem-solving and a
memory task. In the former, he asked players to think aloud when pondering
their next move in a position previously unknown to them—a simple experi-
mental setting, requiring no more than a chessboard, a chess clock, and a
means to record subjects’ statements. In line with Selz’s proposal, players
often used a hierarchy of subsidiary methods. Players also investigated the
same continuation several times, either immediately or after having directed
their attention to a different variation—a process that de Groot named
progressive deepening.
  Not surprisingly, strong players chose better moves than weaker players.
The real question was how this choice took place. It could not be due to
discrepancies in search mechanisms: the protocols did not show any clear
differences between grandmasters and weaker players with variables such
as number of moves anticipated, depth of search, and rate of search. This
result, pointing to the importance of perception, led de Groot to use a second
experimental procedure, a modification of the recall task (Djakow et al.
1927). The crucial improvements were to use positions taken from master
games and to show them only for a brief period of time (from 2 to 15 s). The
results were spectacular: grandmasters were able to reproduce correctly
almost the entire position, while weaker players could retain only a few
pieces. At a more qualitative level, retrospective protocols indicated that
grandmasters and masters were able to understand the gist of the position in
a matter of seconds.
  Together, the thinking-aloud and recall-task results suggested to de Groot
that two ingredients are crucial for becoming a chess master: the development
of a highly elaborated and specific mode of perception, thus allowing a rapid
identification of the essential aspects of a position, and the construction of a
                                      Theories of board-game psychology    37
system of routine playing methods, dealing among other things with strategic
goals and means as well as tactical motives. All this knowledge is stored in
memory and is acquired through experience, that is, dedicated practice, study,
and analysis. De Groot also asserts that chessplayers’ memory can be separ-
ated into explicit knowledge (knowing that . . . ) and intuitive experience
(knowing how . . . ).
   In later research carried out in close collaboration with his student
Jongman, de Groot studied the statistical properties of the chess environ-
ment, in an attempt to answer the question ‘What constitutes a master-like
position?’ (de Groot, 1966; de Groot & Gobet, 1996; de Groot & Jongman,
1966; Jongman, 1968). He also analysed chessplayers’ eye movements in an
attempt to understand their perceptual and memory processes. Finally,
he combined his research in education with his interest in chess, collecting
data about the possibility of transferable benefits from chess instruction
(de Groot, 1977).
   While de Groot did not offer a detailed model of chess thinking, he
elaborated Selz’s theory of cognition in essential ways. Furthermore, he
was the first to emphasize the importance of perception in expert problem
solving. His main conclusions still loom large in current research: expertise
does not derive from extraordinary abilities, either innate or acquired, but
from specific knowledge, in part perceptual, about various aspects of the
task domain. Indeed, de Groot’s influence will permeate almost every page of
this book.


Tikhomirov and colleagues
Since the 1960s, Oleg Tikhomirov has directed a research group at the Uni-
versity of Moscow that has done original work on chessplayers’ cognitive
processes. The group has used a variety of empirical techniques, such as the
analysis of verbal protocols, recording of eye movements (Tikhomirov &
Poznyanskaya, 1966), recording of hand movements of a blind player
(Tikhomirov & Terekhov, 1967), recording of psycho-galvanic reflex in
the study of emotions (Tikhomirov & Vinogradov, 1970), and even the
use of hypnotic techniques (Tikhomirov, 1988, 1990). For Tikhomirov and
his colleagues, the heuristic character of chessplayers’ thinking can be
explained by a complex interaction of emotional, motivational, and cog-
nitive processes. Emotional activation plays a well-specified regulatory func-
tion, and is necessary for productive intellectual activity (Tikhomirov &
Vinogradov, 1970). In line with Gestalt psychology (Koffka, 1935), the
Moscow group proposes that positions are apprehended holistically
(Tikhomirov & Poznyanskaya, 1966). This view led Tikhomirov and his
colleagues to a critique of Newell and Simon’s information-processing
approach (cf. below).
   As noted by Gobet (1993b), an interesting characteristic of Tikhomirov’s
approach, which contrasts with all other approaches reviewed here but agrees
38   Moves in mind
with the Gestalt framework, is that there are few references to memory pro-
cesses. Information is simply assumed to be already present in the environ-
ment, with perceptual mechanisms ready to extract it. Given the importance
placed on memory by researchers of expertise as well as by non-scientific
accounts of chess psychology (e.g., Kotov, 1971), the little weight given to
memory is surprising. In general, while Tikhomirov and his colleagues have
undoubtedly enriched board-game psychology, in particular with non-
standard techniques and novel ideas, it is fair to say that their theories have
not been sufficiently tested by empirical data.


Simon and the Carnegie Tech group
The central question of Herbert Simon’s (1947, 1955, 1956) programme of
research was to find how human beings, in spite of their bounded rationality,
can take reasonable decisions in complex domains and even become experts
in these domains. Given their complexity, combinatorial tasks such as board
games offer an ideal environment for exploring human bounded rationality.
In particular, Simon has used chess to formalize a number of concepts
derived from his theory of bounded rationality, such as presence of goals,
dynamic adjustment of expectations, heuristic search, and satisficing (i.e.,
choice of solutions that are good enough, but not necessarily optimal). He
has also explored how learning mechanisms allow chessplayers to pick up
the regularities from the environment, and, as a consequence, to limit their
amount of search. In most of his research on decision making and expertise
in chess, Simon has used experimentation and computational modelling,
although he has occasionally also drawn on mathematical techniques (Simon,
1974; Simon & Gilmartin, 1973).
   There is a striking similarity between de Groot’s emphasis on selective
search and Simon’s agenda of research into bounded rationality, not to
mention their common interest in chess. Simon was aware of de Groot’s 1946
book by the year 1956 (Simon, 1991) and he was quite impressed by it, to the
point that he organized (and personally carried out part of) its translation
from Dutch into English in 1965. De Groot’s work influenced Simon’s
research in two ways. On the empirical side, it led Simon and his group at
Carnegie Mellon (then Carnegie Tech) in Pittsburgh to carry out memory
and problem-solving experiments with similar methods, including the
extensive use of verbal protocols. On the theoretical side, Simon imported
several ideas from de Groot’s revision of the Selzian framework. In particu-
lar, Selz’s characterization of thought as a sequence of operations is also
apparent in several of the formal models developed by Simon and his
colleagues. An important difference is that Simon’s models were, for the
most part, implemented as computer programs, which allowed their authors
to be much more precise and rigorous than Selz could have been with verbal
descriptions alone.
                                       Theories of board-game psychology     39
Models of heuristic search
The computer models developed by Simon and his colleagues have two
features that differentiate them from other attempts to build chess-playing
computer programs. First, most of them deal with only one aspect of the
game (e.g., find a combination involving a checkmate). Second, and most
importantly, the motivation behind these programs is to understand human
thinking, and not to play strong chess per se. In particular, their behaviour
has been compared with that of human players, for example using verbal
protocols. Two programs, NSS and MATER, are particularly interesting in
this respect.
   The NSS program (Newell, Shaw & Simon, 1958a; Newell & Simon, 1972),
which explores the concept of satisficing, focuses on the role of goals, such as
maintenance of material balance or control of the centre. Based on these
goals, two move generators operate independently: the first generates base
moves (moves at the root of the search tree), and the second generates moves
deeper in the search. Acceptability of the proposed moves is then evaluated
by an independent analysis. Finally, the concept of satisficing is implemented
by having the program choose the first move that reaches a given value.
Although NSS only played a weak game, it demonstrated that a computer
program could find reasonable moves while generating only a small search
tree (less than 100 nodes).
   Like NSS, MATER (Baylor & Simon, 1966) explored only limited search
spaces. It used the heuristic of favouring variations that narrowed down
the number of replies left to the opponent. While excellent in checkmate
combinations with forced sequences of moves, MATER was useless for
other types of positions. To some extent, both programs implemented the
heuristic method of means-end analysis, which was developed more fully in
the General Problem Solving program (Newell & Simon, 1972). In means-end
analysis, the difference between the current and the goal state is noted, and a
subgoal is created to overcome this difference.


Chunking theory
An important means for humans to circumvent the limits of their bounded
rationality is to learn about their environment (Simon, 1956). Thus, it is
only natural that Simon developed a model—the chunking theory
(Chase & Simon, 1973a, 1973b; Simon & Chase, 1973)—which links learning
mechanisms with limited memory and perceptual processes. This theory
proposed that the ability to rapidly recognize important problem features
lies at the core of expertise. This ability is made possible by the acquisition,
over many years, of a large number of perceptual chunks, which act as
access points to semantic and procedural long-term memory (LTM). Chunks
thus serve as conditions of productions, whose actions may be carried out
internally or externally. For example, on recognizing an open line in chess,
40   Moves in mind
a production like ‘IF there is an open line, THEN consider occupying it
with a Rook’ would be executed. This production-system account is linked
to assumptions about learning mechanisms, which are based on the
EPAM (Elementary Perceiver and Memorizer) theory, a general theory of
learning and perception that was originally applied to explain how
people learn verbal material (Feigenbaum & Simon, 1962, 1984). EPAM sees
learning as the incremental and slow creation of a hierarchical discrimination
net.
   The chunking theory postulates two transient memory stores: a short-term
memory (STM), where pointers to LTM are encoded, and a visuo-spatial
memory, called the mind’s eye. The mind’s eye is a relational system storing
perceptual structures both from external inputs and from memory stores.
These structures can be subjected to visuo-spatial mental operations. Finally,
the chunking theory includes parameters specifying learning and accessing
times (e.g., about 8 s to learn a new chunk), as well as memory limits (e.g.,
STM limited to 7 chunks).
   Applied to problem solving in chess, the chunking theory works as follows.
Perception mechanisms allow recognition of patterns of pieces on the board.
These patterns suggest moves, which are used to update the internal repre-
sentation of the board in the mind’s eye. This cycle is then repeated, with the
qualification that pattern-recognition mechanisms now apply recursively on
the internal representation of the position in the mind’s eye. Termination of
search in a branch is obtained by evaluating whether certain goals are above
or below a threshold, whose value may change as a function of the player’s
expectation levels.
   Based on the chunking theory, Simon and Gilmartin (1973) developed a
computer model, called MAPP (Memory-Aided Pattern Perceiver), which
was applied to de Groot’s recall task (see Figure 3.2). Two important features
of the model are that STM is limited to seven items and that learning is slow.
During the recall task, MAPP perceives patterns on the board, and sorts
them through the discrimination net. When an LTM chunk is recognized, a
pointer to it is placed in STM. During the recall phase, MAPP unpacks the
information denoted by the STM pointers. In simulations, MAPP replicated
the performance of a class A player, but could not reach the memory level
shown by a master. Extrapolating from these results, Simon and Gilmartin
suggested that masters’ performance in the recall task requires from 10,000 to
100,000 chunks (they propose to use 50,000 chunks as a first approximation).
They also proposed that these numbers generalize to other domains of
expertise. A weakness of MAPP, in addition to its relatively poor perfor-
mance, was that chunks were selected by the programmers and not acquired
automatically.
   Chase and Simon’s chunking theory has been presented here in some
detail, as it will be used to organize the following chapters. This is a natural
organization: a substantial part of the research on board-game psychology
after 1973 has been done to test aspects of the chunking theory.
                                          Theories of board-game psychology         41




Figure 3.2 Diagrammatic representation of the processes carried out by MAPP.
           The top part of the figure shows the learning phase, during which chess
           patterns are provided so that the discrimination net grows. The bottom
           part depicts the processes carried out by MAPP during a recall task: (a) the
           program detects salient pieces in the stimulus position; (b) the discrimi-
           nation net is provided with the salient pieces and those pieces around them;
           when a chunk is recognized, the net outputs a symbol; (c) the symbols for
           chunks are placed in STM; and (d) the position is reconstructed using
           the symbols found in STM and the chunks associated with them in LTM.
           (After Simon & Gilmartin, 1973.)



Holding’s SEEK theory
An exhaustive review of the literature led Holding (1985, 1992) to the con-
clusion that Chase and Simon’s (1973b) chunking theory did not account
well for the empirical evidence. In particular, he argued that it underestimated
the role of search. Holding’s reanalysis of de Groot’s (1946) data showed
that grandmasters tend to consider more moves and search faster than
Experts. He also noted that de Groot’s statistics were based on a single pos-
ition and that they included a small number of players. These factors could
explain the lack of clear differences between grandmasters and Experts.
Finally, several studies (Charness, 1981b; Holding & Reynolds, 1982; Wagner
& Scurrah, 1971) directly supported the hypothesis that stronger players
search deeper.
   Holding attempted to identify the abilities required for playing chess at a
high level. His starting point was that the basic mechanism of chess skill is to
choose between different moves, and that strong players use their knowledge
to generate a search tree and to evaluate its leaves correctly. The acronym of
Holding’s theory, SEEK, summarizes these ideas: Search, EvaluatE, and
Know. A counterintuitive implication of SEEK is that human experts search
in ways similar to computers: ‘the model simply postulates a tree of move
judgments’ (Holding, 1985, p. 247).
42   Moves in mind
   Although Holding’s book offered an important and influential summary
of the available data anno 1985, several of its conclusions appear debatable
and some of its analyses are considered incorrect (Gobet, 1998b; Gobet &
Simon, 1998b). In addition, given that Holding compared human search with
computer search, a computer implementation would have seemed desirable.
But perhaps the main weakness of Holding’s work is that he has undervalued
the chunking theory. Indeed, all three components of SEEK (search, evalu-
ation, and knowledge) are present in the earlier theory, which also provides
mechanisms linking these components of chess skill, which SEEK does not
(Gobet & Simon, 1998b). Thus, it is the weight given to each of these
components, and not their presence or absence, that differentiates the two
theories.
   Before leaving SEEK, we may mention that Munzert (1988, 1990) has
proposed to integrate the theories of Chase and Simon (1973b) and Holding
(1985). The new framework, which combines pattern recognition, search,
planning, emotion, and action, has had limited impact on the field.


Saariluoma’s apperception-restructuring theory
Saariluoma (1984) conducted a number of experiments addressing the impor-
tance of perception in information processing. For example, he measured
reaction times in tasks where players had to decide whether the white King
was in check or not. He found that strong players are faster than weak players
both in game and random positions, although all players are slower with
random positions. Based on this and similar experiments, Saariluoma
concluded that the mechanisms embodied in MAPP (Simon & Gilmartin,
1973) are valid only for memory encoding, but not for information intake.
To explain these results, he developed a two-component model. First, the
stimulus is encoded; second, a decision is taken (e.g., whether the white King
is attacked or not). Only encoding is a function of expertise.
   Saariluoma (1984, 1990, 1992a, 1995) has proposed a theory of problem
solving based on the mechanisms of apperception and restructuring. The
theory proposes that players, while trying to find a move, access goal positions
by apperception (Leibniz, 1704)—that is, second-order, or conceptual,
perception. They then try to close the path between the problem position
and the goal position, i.e., the problem space that was defined by appercep-
tion. When this is not possible, the problem space is restructured. Thus,
chess thinking may be described as a sequence of apperception-restructuring
cycles that attempts to find a critical path to the goal position. According
to Saariluoma, this mechanism explains why strong players can find solu-
tions with only limited search. This account shares some similarities with
de Groot’s progressive deepening and Newell and Simon’s means-end
analysis (1972), which both make provision for the possibility of problem
redefinitions.
   According to Gobet (1993b), two aspects of this theory warrant further
                                       Theories of board-game psychology      43
elaboration. First, it is debatable whether chessplayers always have a well-
defined goal position in mind and try to eliminate the distance between this
goal position and the problem position. Indeed, de Groot’s (1946) verbal
protocols seldom contain such means-ends analysis behaviour. Moreover,
as noted by de Groot (1946) and Newell and Simon (1972), chessplayers’
thinking is characterized by the presence of several goals, rather than by a
single goal. However, the theory does not make any provision for what
happens when players have no, or several, goal positions in mind. Second,
the relation between apperception and mechanisms commonly proposed in
cognitive psychology to construct internal problem representations is not
always clear. Here, more details about the mechanisms underlying apper-
ception would be welcome. Even so, Saariluoma’s theoretical ideas have
led to the design of innovative experiments, which will be taken up in the
chapters dealing with perception, memory, and problem solving.

Gobet and Simon’s template theory
Gobet and Simon’s (1996c, 2000a) template theory was developed to account
both for the empirical findings the chunking theory could account for and
those that were inconsistent with it. Like the chunking theory, the template
theory asserts that chunks are accessed through a discrimination net. In
addition, chunks that recur often in players’ practice and study evolve into
more complex data structures, called templates. Like chunks, templates hold
information about patterns of pieces. They also contain slots (variables that
can be instantiated) in which new information can be stored rapidly. In par-
ticular, information about piece location or about chunks can be (recursively)
encoded into template slots. As template slots can be filled rapidly, they
essentially enlarge STM for material in the domain of expertise. Templates
themselves are built up slowly and incrementally, at normal LTM learning
rates. Similarly, the pointers contained in the templates are learnt at normal
learning rates. These pointers link to LTM symbols representing moves,
tactical and strategic motives, plans, as well as other templates.
   The template theory intends to combine mechanisms dealing with low-
level cognition, such as pattern recognition, with mechanisms dealing with
high-level cognition, such as the creation and use of schemata. There is much
evidence, discussed in Chapter 5, that strong players use descriptions of a
position that are larger than the four or five pieces proposed by Chase and
Simon. For example, de Groot (1946) suggested that strong players can
rapidly integrate the different parts of the position (roughly, Chase & Simon’s
chunks) into a consistent whole, something weaker players were not able
to do. These integrated representations generally depict typical opening or
middlegame positions. Several features specific to templates capture the
essence of these observations. In particular, templates are quite large (they are
assumed to store at least 10 pieces) and they may be linked to other templates.
   Aspects of the template theory have been implemented in three computer
44   Moves in mind
models: CHREST, CHUMP, and SEARCH. CHREST (Chunk Hierarchy
and REtrieval STructures; Gobet, 1993a, 1993b; Gobet & Simon, 1996c,
2000a; de Groot & Gobet, 1996) implements the learning, perception and
memory mechanisms of the template theory. The main components of the
model are: a simulated eye, a discrimination net, semantic LTM, and a visuo-
spatial STM limited to three items (see Zhang & Simon, 1985, for empirical
support for this capacity). Information within the visual field of the simulated
eye is sorted through the discrimination net. When a chunk is recognized, a
pointer to it is placed into STM, where chunks are treated as in a queue. An
exception is made for the largest chunk met at a given point in time, which is
called the ‘hypothesis’. The hypothesis stays in STM as long as no larger
chunk has been found, and is used to direct eye movements. Every process
in the model is associated with a time parameter. The model also relies on
LTM storage to create a new node in LTM (which takes about 8 s), to add
information to an existing node (about 2 s), or to fill in a template slot (about
250 ms). Learning mechanisms allow the model to automatically create
chunks and templates by scanning a database of master games.
   Computer simulations with CHREST show that the template theory fits
the data on a variety of experimental tasks, such as the pattern of eye
movements, the differential recall of game and random positions, the type
of errors made, the way pieces are grouped during recall, and the recall of
multiple positions (e.g., Gobet, 1993a, 1993b; Gobet & Simon, 1996a, 2000a;
de Groot & Gobet, 1996). The model simulates recall performance from
novice to grandmaster.
   Some applications of the template theory have been aimed at simulating
chessplaying, rather than just perception and memory. CHUMP (CHUnks
and Moves Patterns; Gobet & Jansen, 1994) is a program based on CHREST
that finds moves by pattern recognition alone. It is an implementation of
Chase and Simon’s ideas: given a pattern on the board, a move or a sequence
of moves is proposed. A simple conflict resolution scheme takes care of
cases where several chunks are recognized or where the same chunk elicits
several moves. Given that CHUMP does not carry out search to examine the
implications of the selected moves, its chessplaying ability is limited.
   SEARCH (Gobet, 1997a) is an abstract computer model that extends
aspects of the template theory. It computes behavioural variables as a func-
tion of the number of chunks and templates stored in LTM. These variables
include depth of search or number of moves generated per minute. Like the
chunking theory, SEARCH proposes that information stored in the mind’s
eye decays rapidly, and that it needs to be updated regularly either by inputs
from the external world or by inputs from memory structures. Both models
also propose that search is carried out in a forward fashion, by recursive
application of pattern-recognition processes in the mind’s eye. Templates,
which are present in SEARCH but not in the chunking theory, make search
easier in three ways. First, they make it possible for information to be added
to LTM rapidly. Second, they allow search to be carried out in the template
                                      Theories of board-game psychology    45
space in addition to the move space (cf. Koedinger & Anderson, 1990).
Finally, they counterbalance the loss of information that occurs in the
mind’s eye as a consequence of interference and decay. As shown by com-
puter simulations, SEARCH accounts for various empirical phenomena,
including the small skill difference in average depth of search found in human
chessplayers. As we have mentioned, SEARCH is an abstract model: it was
not made to play chess, but just computes behavioural variables. While this is
obviously a limitation, it should be pointed out that, at the time of writing,
no other computational model of cognition makes similar quantitative
predictions or plays chess.


Influences from other theories of cognition
In the previous section, we reviewed a number of theories that have been
applied to explain phenomena in the psychology of board games. Several
of these theories were later used to explain other phenomena as well, both
within and outside the field of expert behaviour. In this section, we move
across the fields in reverse, so to speak, and review a number of theoretical
frameworks that have been developed with different phenomena in mind,
but have sometimes been used in the literature on board-game psychology.
We start with theories in cognitive psychology, and then consider theories on
intelligence and development.


Skilled memory and long-term working memory
After a comparison of experimental results, Miller (1956) suggested that
the human mind can recall only about seven items when they are presented
rapidly. Research into two expert populations (board-game masters and
mnemonists) has shown that this limit is not immutable but can be overcome
with practice. For example, Chase and Ericsson (1981, 1982) trained college
students, over long periods of time, to memorize a large number of random
digits dictated one per second. The best participant was able to memorize
up to 106 digits while Miller suggested a maximum of nine. In the ‘skilled
memory theory’ that flowed from this research, Chase and Ericsson proposed
three principles to explain extraordinary memory for digits: the importance
of deliberate practice for acquiring a large number of chunks; the presence of
‘retrieval structures’ (i.e., stable LTM structures for rapidly indexing new
material), and the speed up of mental operations with practice.
   Ericsson and Kintsch’s (1995) long-term working memory theory is a
modification and expansion of skilled memory. One of the goals of the
theory was to show that the principle of retrieval structures applies to
domains beyond expert behaviour, such as text comprehension and memory
in general. Ericsson and Kintsch consider chess as one of the domains best
supporting their theory. They propose that skilled players have constructed a
hierarchical retrieval structure, similar to the 64 squares of the chessboard,
46   Moves in mind
which allows players to update information rapidly during search. The
theory also proposes that chessplayers can create new LTM associations
rapidly, although no parameter is given to specify this speed of encoding.
The similarities and differences between long-term working memory and the
template theory are discussed in detail in Ericsson and Kintsch (2000), Gobet
(1998b, 2000a,b,c), and Gobet and Simon (1996c).


Knowledge-based theories
These theories address the role of high-level, conceptual knowledge. Where
the chunking theory emphasizes the quantitative amount of knowledge
necessary to reach expertise, they stress its qualitative organization. A nice
example of this line of research is the study by Chi, Glaser, and Rees (1982),
who demonstrated that experts tackle physics problems at a more abstract
level than novices, using basic principles of physics such as the equilibrium
of forces. By contrast, novices pay attention mostly to surface features. In
addition, knowledge representation influences the flexibility with which
problems are represented and the type of search used (Larkin, McDermott,
Simon, & Simon, 1980). Several formalisms imported from artificial intelli-
gence have been used to model experts’ knowledge and its hierarchical
organization, including production systems, semantic networks, frames, and
trees (see Jackson, 1990; Reitman-Olson & Biolsi, 1991; or Stefik, 1995).
   This paradigm has been used in a number of studies on board games. For
example, Cooke, Atlas, Lane, and Berger (1993) and Holding (1985)
emphasize high-level, schematic structures in chess, and Yoshikawa, Kojima,
and Saito (1999) speculate about the knowledge organization of Go players.
While this approach could, in principle, coexist with the chunking theory—
after all, Simon was a key player in both approaches—it has evolved in an
independent direction. Knowledge-based theories have had their impact on
research into memory and learning, with limited repercussions on problem
solving and decision making.


General theories of intelligence and talent
One of the oldest and most controversial questions in psychology is whether
intelligence and talent are innate or acquired through interaction with the
environment. This debate, and a number of theories enmeshed in it, will be
considered when dealing with education and intelligence (Chapters 8 and 9).
In these domains, as elsewhere in psychology, the debate is far from having
been resolved, and data based on genetics (e.g., Plomin & Petrill, 1997) are
countered by data showing the flexibility and plasticity of the human mind
(e.g., Ericsson & Lehmann, 1996). Several theories of intelligence have sug-
gested that the human mind can be partitioned into a number of components
or faculties (e.g., Gardner, 1983); of these, visuo-spatial and mathematical
abilities have often been proposed to be essential for board games. Finally,
                                      Theories of board-game psychology     47
chess and Go have recently been used to support the hypothesis that the level
of general intelligence is rising (Howard, 1999, 2001).

Connectionist accounts
Many of the theories we have considered so far would accept the need for
some kind of symbolic processing, as described, for example, in Newell and
Simon (1972). A mini-revolution occurred in cognitive science in the 1980s,
when a number of theories proposed that human cognition can be seen as the
parallel processing of a large number of neuron-like units connected by
links. Several authors (e.g., Dreyfus & Dreyfus, 1986; Holyoak, 1991) have
suggested that phenomena such as expertise can be captured by these models,
but not by standard symbolic approaches. Intuition in board games, in
particular chess and Go, has often been used as a paradigmatic example of
what can uniquely be explained by connectionist models.
   As the models discussed in this book show, it is rather the opposite that
happened. There exist a number of symbolic models that explain aspects of
expertise in board games, while there are few connectionist models that can
successfully replicate human data. In most cases, these models addressed
technical questions about connectionist processing without convincingly
creating a link with human data (e.g., for chess, Hyötyniemi & Saariluoma,
1998; Lories, 1992; Mireles & Charness, 2002).


Theories of development and environment

Developmental theory of Piaget
Piaget’s theory of cognitive development has played an influential role in
psychology in the twentieth century, and we can only give a brief summary
here. Piaget (e.g., 1936, 1970) proposed that adaptation occurs whenever the
interaction between an organism and its environment modifies the organism
so that its chances of survival are increased. Biological and cognitive adapta-
tions are made possible by two fundamental mechanisms—assimilation
and accommodation—which are complementary and inseparable. With
accommodation, an organism changes its internal structure as a function
of the properties of an external object. With assimilation, it changes the
object so that it fits into its own structures. Adaptation is reached when an
equilibrium is reached between the two mechanisms. Structures are needed
for assimilation and accommodation to operate on, and these are offered by
the schemes, which ‘refer to classes of total acts, acts which are distinct
from one another and yet share common features’ (Flavell, 1963, p. 54). In
addition, Piaget saw development from childhood to adulthood as the
transition through four main stages, culminating in the ‘formal-operation’
stage, which is characterized by hypothetico-deductive reasoning, and the
capability to think using abstract possibilities.
48   Moves in mind
   A weakness of Piaget’s theory is that the concepts of assimilation and
accommodation have not been specified with sufficient detail (e.g. Flavell,
1963; Klahr, 1995). A recent attempt to formalize these two mechanisms has
been made within the EPAM/CHREST framework, which, as we have seen
earlier, originated from board-game research (Gobet, 1999a).
   Piaget himself was interested in games based on rules (which certainly
include board games) as a new category of behaviour appearing in middle
childhood. As Cole and Cole (2001, p. 558) mention, Piaget ‘saw the ability to
engage in rule-based games as a manifestation of concrete operations in the
social sphere, corresponding to decreasing egocentrism’. Several Piagetian
concepts could be applied to board-game psychology: cooperation, decen-
tration, operations, and abstraction. Indeed, board games, which require
planning, hypothetico-deductive thought, and the construction of a search
space consisting of possible moves, seem to offer an ideal domain to test
some of Piaget’s ideas, in particular the notion that formal thought appears
relatively late in development (about 12 years of age). Chapter 7 reviews all
works we could find in which children’s development is studied alongside
their ability to play board games. Given the direct relevance of board games
for evaluating the Piagetian framework, it is surprising that more research has
not been carried out.


Role of the environment
Several theorists have proposed that an analysis of the environment should
play an important role in psychological theorizing. The extreme position
is that knowledge of the statistical structure of the environment is sufficient
for predicting behaviour (Anderson, 1990b; Brunswik, 1956; Gibson, 1979).
A more balanced position suggests that psychological theories should com-
bine assumptions about the environment with assumptions about internal
mechanisms. For example, Simon (1955, 1956, 1969) has proposed that
learning the properties of the environment is an essential mechanism for
compensating the limited nature of human rationality.
   Within the realm of board-game psychology, both positions have been
defended. On the one hand, as we have seen in Chapter 2, a number of re-
searchers (e.g., de Groot & Gobet, 1996; de Groot & Jongman, 1966; Holding,
1980; Jongman, 1968; Retschitzki, 1990; de Voogt, 1995) have analysed the
environments generated by board games along a number of dimensions,
including their statistical regularities and amount of complexity. While
obviously interested in the game environments themselves, all these authors
also did such analyses to understand cognitive processes better. Simon and
Gilmartin (1973) carried out a different type of analysis and estimated
the number of chunks necessary to reach mastership in chess, based on
mathematical assumptions about the environment. Again, this was done
with cognitive processes in mind—in this case, a better understanding of the
memory mechanisms underlying masters’ performance.
                                      Theories of board-game psychology    49
   On the other hand, Vicente and Wang (1998), in their constraint-
attunement theory, apply the Gibsonian approach to explain expert memory
for chess positions. They argue that it is necessary to analyse goal-relevant
constraints within the structure of the environment before proposing theories
of expert behaviour referring to cognitive mechanisms. As is apparent in this
book, we believe that the best approach consists in combining the analysis of
the environment with the construction of detailed process models. The reader
interested in these questions is referred to the discussion following Vicente
and Wang’s article (Ericsson, Patel, & Kintsch, 2000; Simon & Gobet, 2000;
Vicente, 2000).


Cross-cultural psychology
Cross-cultural psychology studies the relationships between psychology
and culture. Note that nationality is inadequate for a definition of culture
(Irvine & Berry, 1988; Poortinga, 1977), and that the environmental variables
identified in cross-cultural psychology also include socio-economic factors,
family size and education or dispositional variables like gender and age
(Irvine & Berry, 1988, pp. 25–7). The role of culture in cognitive research on
expertise has not received much attention. Research on genius (Simonton,
1984) or cognition and culture in general (Altaribba, 1993; Irvine & Berry,
1988) address few of the issues that appear relevant for experts of board
games. Board-game research in cross-cultural settings often requires
modification of the research method used, which may prohibit experimental
tests of theoretical constructs.


Conclusion
This chapter has provided a brief history of board-game research, and has
presented the main theories that have been advanced to explain skilled
behaviour. While a variety of theories have been applied to a variety of board
games, most research has been carried out into chess, with the chunking
theory as a theoretical framework.
   A quick look at the reference list indicates that research output had been
rather weak until the mid-1960s (at most one publication a year), became
stable from the mid-1960s until the mid-1980s (about five publications a
year), but has exploded since then (see also Gobet, 1993b). In 1990, Pertti
Saariluoma organized an International Symposium on the Psychology of
Chess Skill in Helsinki, and several contributions of this symposium were
published in a special issue of Psychological Research (Vol. 54, 1992).
Psychology is also represented in the International Colloquia Board Games
in Academia and the Journal of Board Games Studies.
   The field has also had an impact on cognitive science and psychology at
large, as documented in some detail by Charness (1992). For example, the
classic works of de Groot and Chase and Simon are mentioned in textbooks
50   Moves in mind
of cognitive psychology, and are often cited in the literature. Recently, chess
has been the focus of several theoretical debates, such as that about Vicente
and Wang’s (1998) constraint-attunement theory and Ericsson and Kintsch’s
(1995) long-term working memory theory.
  Sufficient background knowledge has been provided so that we can
now address the detail of the results. We consider first low-level aspects of
cognition, and then move to higher aspects. Accordingly, we start our journey
with the problem of perception and categorization.
4      Perception and categorization




The rapidity with which a Kasparov in chess or a Sijbrands in international
draughts evaluates a position and chooses a strong move has done much to
attach the label of ‘genius’ to these players. Indeed, de Groot (1946) noted
that world champion Max Euwe had as much understanding of a position
after five seconds as a strong amateur after 15 minutes. How can we explain
this rapid perception and categorization of a position?
   While popular with laypeople, the innate-talent hypothesis has not been
successful in accounting for expert perception (see Chapter 9). Starting
with de Groot, preference has been given to explanations stressing the role
of practice in developing a ‘professional eye’. In a nutshell, the idea is that,
through dedicated practice and study, chess masters acquire both a large
knowledge base and a considerable number of perceptual cues that allow
them to rapidly access the relevant information. This explanation has been
applied outside the realm of board games to explain the almost instant-
aneous understanding of routine problem situations shown by experts in
domains such as physics, medicine, and electronics.
   Several characteristics of board-game players’ perceptual mechanisms
have been identified, using measurements such as eye-movement recordings,
reaction times in discrimination tasks, and recall performance in memory
tasks with brief presentations. In general, the empirical results support de
Groot’s hypothesis: players, as they develop higher skills, acquire finely tuned
perceptual mechanisms. In this chapter, we review the available empirical
evidence, starting from low-level perception (e.g., eye-movement records)
up to high-level perception (e.g., use of concepts), before considering the
theoretical impact of these results.


Low-level perception
Two techniques prevail in the study of low-level perception: eye-movement
recordings, and reaction-time experiments. We consider these techniques in
turn. (Chapter 6 will discuss further experiments using eye movements.)
52   Moves in mind
Eye-movement studies
The key assumption in eye-movement recording, well supported by the data,
is that eye fixations are good indicators of where attention is directed, and,
that they therefore offer valuable information about cognitive processes
(e.g., Kennedy, Radach, Heller, & Pynte, 2000; Monty & Senders, 1976). In
addition, they have a fine-grained time resolution and thus can beneficially
complement larger grain methods such as verbal protocols. Given that board
games are highly visuo-spatial, one could have expected that eye-movement
recordings would have been a popular research tool. However, until recently,
data on the eye movements of board-game players have been scarce. This
dearth of data may be due to the technical difficulties associated with the
collection of eye movements, although, with technological improvements,
these difficulties have considerably diminished. All the data available are
concerned with chess.
   In the experiments we are about to describe, the board was static, and the
player’s head held stationary. Eye movements consist mainly of short saccades
and longer fixations. During a saccade, the eye jumps from one location to
another. A saccade lasts for about 30 to 50 ms, during which time little, if any,
information is picked up. During a fixation, the eye remains focused on one
point of the display. The duration of fixations, which is more variable than
that of saccades, depends on the type of task, the instruction, and other
features of the experimental design. In tasks with a stationary display such as
reading, the average duration of fixations is about 250 to 300 ms.


Heuristics of the professional eye
De Groot and Gobet (1996) recorded the eye movements of five masters and
three weak players during the brief presentation (5 s) of a position. Each of
the six positions was taken from a master game, after about 20 moves. After
players had finished reconstructing the position, they provided a retrospective
protocol by attempting to recall where they had focused their attention
during the initial presentation of the position. De Groot and Gobet identified
a few striking skill differences. On average, masters had shorter fixations
(260 ms vs. 310 ms), and their fixations showed smaller standard deviations
(100 ms vs. 140 ms). De Groot and Gobet took these results as supporting
the hypothesis that masters have a smoother and more controlled process.
A clear difference was also found for the percentage of the board covered by
eye fixations and the (chess) importance of the squares covered. Finally,
although masters were more efficient than weak players in the way they
scanned the board, there was no correlation between accuracy of recall,
and what pieces had been seen (either focally or peripherally). Figure 4.1
illustrates some of these results.
   Analyses carried out on geometric aspects of eye movements identified
reliable skill differences. The distance between fixation points was smaller for
Figure 4.1 Examples of human eye movements (novice and master) and simulated
           eye movements. The shaded squares indicate important squares in the
           position, and the diameters of the circles are proportional to the fixation
           time. The first fixation is always located in one of the four central squares.
           (Adapted from de Groot & Gobet, 1996.)
54   Moves in mind
weak players than for masters, and the analysis of the angle formed by triples
of fixations showed different distributions, weak players tending to have
small angles. Although the recording equipment was not sophisticated by
today’s standards, the results also showed that masters tended to fixate
more often at the intersection of squares, perhaps an indication that they
perceived chunks of pieces rather than single pieces (a similar result has been
found in a different task by Reingold, Charness, Pomplun, & Stampe, 2001;
see below). There was also an unexpected result. Several authors (e.g.,
Holding, 1985; Simon & Barenfeld, 1969) have proposed that masters have
more eye fixations along ‘lines of force’ (i.e., along a Rook’s horizontal or
vertical line). This hypothesis was not supported by de Groot and Gobet’s
eye-movement data.
  In summary, many variables related to eye fixations discriminate reliably
between stronger and weaker players. These differences are partly due to
the different perceptual heuristics used during the first seconds of seeing a
position, with weaker players tending to look only at one portion of the
board. They also suggest that the knowledge acquired by players help guide
their eye movements. This idea has been directly tested with CHREST.


Simulating the professional eye with CHREST
While CHREST (see Chapter 3) is mainly a model of learning and memory,
it can also simulate chessplayers’ attention mechanisms and eye movements
(de Groot & Gobet, 1996). As we have seen, masters and novices follow
different goals when viewing a board. This is reflected in CHREST by dif-
ferent mechanisms. In the early fixations, where perceptual saliency may be
prominent, the version simulating the masters gives precedence to colour
contrasts. Later eye fixations are controlled by the ‘hypothesis’ (i.e., the
largest chunk met so far). With this mechanism, the next eye fixation and, as
a consequence, attention, are directed by the structure of the discrimination
net. This mechanism generates about 75% of the eye movements when simu-
lating masters (almost none with novices). When the first two mechanisms
do not apply, the model falls back on three heuristics, which are used with
equal probability: fixations along relations of attack and defence; fixations in
the periphery; and fixations towards as yet unknown portions of the board
(this could be called the novelty heuristic). When simulating eye movements
of novices, the model follows almost the same set of heuristics, with two
differences: perceptual saliency consists in piece size, not in colour contrast,
and the novelty heuristic is not employed.
   Two nets were used in the simulations reported by de Groot and Gobet
(1996). The version simulating novices had about 200 nodes, and that simu-
lating masters had about 25,000 nodes. The novice version was slower than the
master version at moving a piece in the mind’s eye (this is consistent with
empirical data; see de Groot & Gobet, 1996, pp. 236–8). When tested on the
same positions as the human subjects, CHREST was able to successfully
                                             Perception and categorization    55
simulate all the main quantitative results observed with humans, reproducing
both the skill effects and the absolute values of the variables under study,
such as the mean and standard deviation of the fixation times. In particular,
the model simulating the masters carried out eye fixations that were smoother
than those of the novice model, were about 50 ms faster, and showed less
variability. In addition, the master model covered more squares than the
novice model, and showed a better correlation between the squares covered
and the chess value of these squares (see Figure 4.1). Based on the simula-
tions, de Groot and Gobet concluded that simple mechanisms are sufficient
to account for the masters’ selective eye movements. These mechanisms
combine knowledge-based heuristics with heuristics taking advantage of per-
ceptual features of the environment.

Eye movements and retrospective protocols
De Groot and Gobet (1996) were also interested in combining eye-fixation
recordings with retrospective verbal protocols. Since this methodology can
be used for studying cognition beyond board games, we present it in some
detail here. As we have seen earlier, eye movements offer powerful measures
of cognitive processes. Similarly, although this is more controversial, retro-
spective verbal protocols can provide valuable insight into subjects’ thoughts,
in particular in tasks where the use of concurrent protocols is not possible
(e.g., tasks that are highly visuo-spatial or of short duration). In the study of
expertise, retrospective verbal protocols offer information that could hardly
be obtained by experimental means only. De Groot and Gobet claim that
the joint application of these two techniques could remove some of the
weaknesses of each technique taken in isolation. Eye movements can be
used to validate retrospective protocols; through a comparison of the eye-
movement trace and the contents of the retrospective protocol, it is possible
to assess the accuracy of the verbal report. It is also possible to fill in gaps
in the retrospective protocols, thereby enabling a faithful account of what
the subject has done during the task. Thus, this methodology may be used
to test hypotheses about how players memorize aspects of the task and to
give insight into what players are conscious of. Conversely, retrospective
protocols can help validate eye movements. Although progress has been
made in eye-movement registration, noise still hampers the interpretation of
this type of data. Retrospective protocols thus help clarify ambiguities in the
eye-movement protocols.
   De Groot and Gobet substantiated these claims by first recording eye
movements during the five-second presentation of a position, and then
asking players to retrospect after its reconstruction. Although chess is mainly
a visuo-spatial task, eliciting verbal protocols did not turn out to be a
problem, because chessplayers have learnt—by reading books or talking
to colleagues, among other things—to ‘talk chess’. It was found that some
players had a remarkable memory of their eye movements, while others had
56   Moves in mind
a poor recollection. Players tended to report that they had seen perceptually
salient aspects of the position early on, although this was not always
corroborated by the eye-movement record. Another intriguing result was
that players, when they have visited the same square twice or more, tend to
mention only the first fixation in their protocol. This phenomenon is similar
to the ‘Ranschburg effect’ identified in memory experiments, where repeated
items presented in short sequences are recalled poorly.


Recent eye-movement studies
Reingold et al. (2001) employed eye movements to study the perceptual
differences elicited by structured and random chess positions. They used a
combination of the change-blindness paradigm and the gaze-contingent
window paradigm. Change blindness refers to the difficulty that humans have
in detecting striking changes to objects and scenes, when these changes
coincide with an eye movement or a flashed blank screen. In the gaze-
contingent window paradigm, the portion of the display (window) in which
the information is clearly visible is modified in real time after each fixation. In
Reingold and collegues’ experiment, the window was centred on the point of
fixation, and chess pieces lying outside the window were replaced by grey
blobs. Players’ visual span was measured by varying the size of the window
and determining the smallest window that did not affect players’ performance
in detecting minor changes in the position (these changes could happen either
inside or outside the window). Results show that experts had larger visual
spans with structured, but not random, positions. This suggests that, in the
former case, the players were able to attenuate change blindness by improving
target detection. Reingold et al. also carried out a check-detection task on a
reduced 3×3 board with a King and one or two potentially checking pieces.
Experts made fewer fixations per trial, and, as in de Groot and Gobet’s (1996)
experiment, fixated more often between pieces than on the pieces themselves.
The results were interpreted as strong support for acquired perceptual skills
that allow experts to encode the position rapidly, as opposed to domain-free
perceptual or memory skills.


Scanning behaviour in Go and gomoku
Eisenstadt and Kareev (1977) studied players’ scanning behaviour during
a game. They used a movable one-by-one-square window, where only one
square could be seen at a time. Players used a light pen to select which square
they wished to see. This apparatus was assumed to approximate more
sophisticated eye-recording techniques. Four main types of scanning were
identified: (a) confirmatory scan, where the player tested an hypothesis about
the location of a piece; (b) exploratory scan, where the player looked at
various squares without any particular hypothesis in mind; (c) revival scan,
where the player looked again at a square he had recently visited; and (d)
                                            Perception and categorization    57
imaginary scan, where the player, planning a move, pointed to a square where
he had mentally placed a piece. These four types of scan were built into a
computational model, which also included assumptions about the size of
the fovea (the central region of the retina, where vision is most sensitive
to colours and details), working memory, and long-term memory. To our
knowledge, the performance of this model has not been compared with
human data formally.


Identifying pieces and detecting attack
Does practice affect low-level perception? The available evidence indicates
that this is the case. For example, Saariluoma (1984) showed that chess
masters are faster than weaker players at counting the number of Bishops
and Knights on the board and at deciding whether the King is attacked.
An interesting side result is that, although masters are slower with random
positions than with game positions, they are still reliably faster than weaker
players.
   Similar results were obtained by Fisk and Lloyd (1988), who were inter-
ested in how novices learn the movements of pieces in a pseudo-chess
environment, and in how they create automatisms. During the experiment,
which lasted for 864 trials distributed in 1.5 hours, participants were pre-
sented with a board containing six pieces, represented as letters, and a target,
represented by the letter T. They had to decide which piece could take
the target. The pieces moved as in chess. Results show the typical power law
found in many learning experiments, with rapid speed-up in reaction time
and decrease in the number of errors at the beginning followed by slower
improvement thereafter. At the end of the experiment, the participants were
as fast as intermediate-level chessplayers, but slower than masters.
   In Kämpf and Strobel’s (1998) experiment, two groups of players (masters
and advanced amateurs) had to detect as soon as possible whether or not a
piece had changed its location in a position previously shown for 25 s. All
positions contained a possible combination, although this was not mentioned
to the players. Three variables were manipulated: the number of squares the
piece had been displaced, whether or not the target piece was involved in the
combination, and whether or not the piece after its displacement disturbed
the combination. Kämpf and Strobel found that the latencies were shorter
with distant and involved pieces. Masters, but not amateurs, appeared to
benefit from changes disturbing the combination.
   Reingold, Charness, Schultetus, and Stampe (2001) used a check detection
task with a reduced chessboard (5×5 squares). In the first part of the experi-
ment, the board contained the black King and one or two potential checking
pieces. The task was to determine as quickly and accurately as possible
whether the black King was in check. Variables of interest included the
presence or absence of a check and the number of attackers (one or two).
Results show that, overall, experts were faster than intermediates and novices,
58   Moves in mind
and that all players were slower when there were two potential attackers. The
crucial conditions were those with two pieces; the presence of perceptual
chunks would predict that experts can encode the information in parallel and
answer ‘No’ or ‘Yes’ in similar time, while novices would have to carry a serial
search, and therefore be slower with ‘No’ answers. This is because, with ‘Yes’
answers, they will pick up the checking piece first half of the time by chance.
With ‘No’ answers, they will have to pay attention to both pieces to make sure
that none of them is giving check. As predicted, with novices, the reaction
time cost for adding a distractor was differentially greater in trials where
participants had to answer ‘No’ than in trials where they had to answer
‘Yes’. This interaction was not found with experts. Reingold et al. considered
this result as evidence for superior perceptual encoding by experts. However,
they do not discuss why experts, like other players, are globally slower with
two pieces than with one.
   The second part of the experiment aimed to induce a Stroop-like effect
with chessplayers. This effect denotes the phenomenon where skilled readers
cannot avoid encoding word meanings automatically, even though this may
lead to inferior performance. In the classic example, participants have
to name the colour in which a word is printed as rapidly as possible, while
ignoring the meaning of the word (e.g., with BLUE printed in green, the
answer should be ‘green’). Reingold et al. (2001) cued one of two potential
attackers by colouring it in red; the task was to decide whether the cued piece
was attacking the black King, ignoring the other piece. Experts derived no
benefit from highlighting, while both intermediate and novice players
did. Indeed, the strong skill effect in the baseline condition (‘No’ answers
without highlighting) totally disappeared when one piece was highlighted.
A Stroop-like interference effect was found on incongruent trials in which a
cued nonchecking attacker appeared together with an attacker that was
checking; in this case, experts were reliably slower than the baseline (a
reaction-time increase of 144 ms). Again, these results were taken as indica-
tive of automatic and parallel encoding of chess relations with experts.
   Even though aspects of perception can be improved with learning, it seems
that some basic principles—the so-called Gestalt principles (e.g., Koffka,
1935)—do not differ much across skill levels. Three principles are of particu-
lar interest for the perceptual processes used in game playing: proximity,
similarity, and good continuation. The principle of proximity is assumed to
perceptually group elements that are near to each other. The principle of
similarity is assumed to group similar elements. And the principle of good
continuation is assumed to group elements that lie along straight or smoothly
curved lines.
   Two studies (Eisenstadt & Kareev, 1977, with gomoku and Rayner, 1958a,
with pegity) showed that these principles influence perception in board
games. The goal of these games is to connect pieces in a row or in a diagonal
line (in any direction). It was shown that it is harder to perceive dangerous
alignments of pegs on diagonals than along horizontal and vertical axes
                                            Perception and categorization    59
(principle of proximity), and that it is more difficult to perceive these patterns
when the pieces composing them are in noncontinuous locations than
when they are in continuous locations (principle of good continuation and
similarity). Similar phenomena occur in chess (de Groot & Gobet, 1996).
For example, Gestalt principles can explain that even novices tend to recall
Pawn chains, which satisfy the principle of good continuation and similarity,
and that players’ attention tends to be directed to pieces located among the
opponent’s pieces, which provide a strong perceptual contrast.


High-level perception and categorization

Recognizing key features of a position rapidly
As noted in Chapter 3, de Groot (1946) found that chess masters can
memorize a position rather well even with a presentation time as short as
2 s. Recently, Gobet and Simon (2000a) have replicated this result with a
presentation time of 1 s. Although their recognition is not always accurate,
masters tend to identify the key features of the position, such as the type of
opening or the main strategic plans, even with such a short presentation time.
   Chessplayers can memorize chess-relevant information with even shorter
presentation times, at least with partial chessboards. Using a 4×4 board, Ellis
(1973) showed that good amateurs are able to memorize the position with
reasonable accuracy even after a very brief exposure (150 ms). Again, these
results suggest that skilled players have developed automatic recognition
processes. As discussed below, this feature is well captured in Chase and
Simon’s (1973b) chunking theory and its outgrowth, the template theory.
   Masunaga and Horn (2000) conducted a large study aimed at studying
the link between intelligence and expertise in Go. They submitted 263 male
players at 48 levels of expertise, from beginners to professionals, to a number
of tasks. An originality of the study was that each task was carried out with
both Go and control material. In a task measuring the speed in identifying
Go patterns, players had to find and identify important stone configurations
(called ‘atari’) as rapidly as possible from a set of patterns that contained
foils. There was a reliable skill effect, with a clear difference between pro-
fessionals and other players. No difference was found between beginners and
intermediates. Finally, there was no difference in a control task where partici-
pants had to find a particular letter in a page containing 600 Japanese letters.
   Another task involved the comparison of pairs of Go configurations.
Players had to decide as rapidly as possible if two configurations were the
same or different. Again, there was a skill effect, with professionals being
quicker than the other groups. There was no skill difference in a control task
where participants had to compare pairs of strings of Japanese letters.
   Anecdotal evidence for perceptual speed also comes from mancala games.
In these games, a characteristic of skilled play is to know at a glance how
many seeds a hole (called ‘odu’ in ayo and ‘kroo’ in awele) contains, without
60   Moves in mind
counting. Commenting about ayo, Odeleye (1979, p. 52) explains this feat by
the ability of good players to keep track of the number of seeds placed in a
given hole, updating this number after each move. Some skilled players are
able to tell the exact number of seeds in an odu immediately, even without
having seen its gradual filling. According to Odeleye, players acquire this
difficult skill, as well as a thorough mastery of the game in general, through
practice over many years. Experiments could be carried out to test Odeleye’s
assertions.


Evidence for chunking: Chase and Simon’s experiments
If skilled players can develop highly efficient perceptual skills, it is necessary
to find means to measure these skills experimentally and to identify the
mechanisms that enable them to develop. This is the problem that Chase
and Simon tackled in three seminal papers (Chase & Simon, 1973a, 1973b;
Simon & Chase, 1973).
   Chase and Simon (1973a) videotaped players’ behaviour in two tasks:
a ‘memory’ task (the classic recall task of de Groot), and a ‘perceptual’ task,
where a stimulus position had to be copied on a different board. In both
cases, they used game and random positions. They then coded the time
needed between the placement of each piece within a pair of pieces. This
allowed them to compare the distribution of latencies in both tasks. A key
prediction of the chunking theory was that pairs of pieces that share
numerous relations are more likely to be noticed together, and, as a con-
sequence, chunked. (Chase and Simon used the following relations: attack,
defence, proximity, same colour, and same type.)
   To test their hypothesis, Chase and Simon analysed the chess relations
between successively placed pieces in the two tasks. Two pieces were deemed
to belong to the same chunk when they were replaced within a single glance
in the perceptual task, or with an interval less than 2 s in the memory task.
Pieces were otherwise deemed to belong to two different chunks. Chase and
Simon found that the chess relations between successive pieces were more
frequent within a chunk than between two chunks. These results, which were
obtained with only three subjects (a master, a class A player, and a novice),
have recently been replicated by Gobet and Simon (1998a) with a larger
sample (26 players), and with the use of a computer to display the stimuli
and record the results. The close link between the two criteria—latencies and
number of relations shared—has been found in other domains, such as in
verbal and pictorial recall tasks that involve semantic clustering (Wixted &
Rohrer, 1994).


Additional evidence for perceptual chunks in chess
The psychological reality of chunk structures has been established with other
experimental paradigms as well. The first direct manipulation of chunks
                                            Perception and categorization    61
was done by Charness (1974), who presented pieces verbally, at a rapid rate
(2.3 s per piece). Pieces were either grouped by the experimenter, following
the chunking relations proposed by Chase and Simon (1973a), ordered by
columns, or dictated in random order. Charness observed the best recall
performance in the chunking condition, followed by the column condition.
The poorest recall occurred in the random-order condition. Charness found
the same results when pieces were presented visually, one at a time.
   Frey and Adesman (1976) obtained similar results. They presented chess
positions incrementally using slides, each adding a group of (usually) four
pieces (i.e., a new slide retained the pieces from previous slides). Each of the
six slides for a position was presented for 2 s. Chunk presentation produced
better recall than column presentation, and, somewhat surprisingly, better
recall than presentation of the entire position for the same length of time
(12 s). The latter result suggests that position decomposition, helped by
chunk presentation, may be either problematic or time consuming for
some players.
   Chi (1978) applied to chess the partitioning technique devised by Reitman
(1976) for studying Go memory (see below). She first asked her subjects to
memorize briefly presented positions, and recorded the latencies during the
piece placements. Then, she gave them the diagram of the positions, and
asked them to draw boundaries around the clusters of pieces they perceived
as meaningful. Chi found two important results. First, clusters did sometimes
overlap (which was also found in computer simulations using the chunking
approach; see de Groot & Gobet, 1996), something that Chase and Simon’s
technique could not capture. Second, comparing the results of both tasks,
Chi found that, in the recall task, subjects took longer, on average, to place
pieces crossing a chunk boundary (about 3 s) than to place pieces within a
chunk (around 1.5 s). As noted by Chi, this finding is consistent with Chase
and Simon’s (1973a) estimate that retrieval of pieces within a chunk takes less
than 2 s, and that retrieval of a new chunk necessitates at least 2 s.
   Freyhoff, Gruber, and Ziegler (1992) used a similar partitioning procedure,
but added two conditions: first, subjects had to divide the clusters obtained in
a first partition into subclusters; second, they had to combine the original
clusters into superclusters. Masters produced larger clusters at all levels of
partitioning than did class B players. In addition, the clusters produced at
the basic level (that is, in the first partition) corresponded rather well to the
chunks identified by Chase and Simon (1973a). In the Freyhoff et al. study,
the average size was 3.6 pieces for masters, and 2.7 pieces for class B players—
reasonably close, given differences in the positions and in the methodology
used, to Chase and Simon’s 2.5 pieces for the master and 2.1 pieces for the
class A player. Moreover, the distribution of relations between pieces was
similar to that found by Chase and Simon. For example, in Freyhoff and
colleagues’ data, 74.6% of the pieces within a partition shared three or more
relations, as compared to 67.6% in Chase and Simon’s data for the pieces
within a chunk in the recall task.
62   Moves in mind
   Gold and Opwis (1992) used the statistical technique of hierarchical cluster
analysis to identify chessplayers’ chunk structures. As variables, they chose
the locations of pieces on the board, and, as values, they used the correct
or incorrect recall of these pieces. To estimate the similarity between two
pieces, they aggregated over subjects the frequency with which these pieces
were either both placed correctly or both placed incorrectly. The clusters
obtained with this technique yielded stable partitions, which were easily
interpretable. Overall, these clusters were similar to those identified by
latencies (e.g., castled positions, chains of Pawns, common back-rank piece
positions).
   In general, the experiments just reviewed support the psychological reality
of chunks as defined either by number of (chess-) meaningful relations,
partitions, or latencies in placement. But chunks do not tell the whole story.
As we shall see below, there is also strong evidence for high-level knowledge
structures. And a surprising outcome, given the empirical and theoretical
importance of chunks, is that they appear rarely in masters’ (retrospective)
verbal protocols. As we saw earlier, de Groot (1946) and de Groot and Gobet
(1996) asked masters to retrospect after the brief presentation and recall of
a position. While masters often gave high-level descriptions, such as type
of opening or main strategic plans, they almost never mentioned clusters of
pieces sharing relations of defence, attack, and proximity. The closest to
chunks was what de Groot and Gobet call ‘visual images’, which occurred
about once per protocol. In these visual images, perceptual properties such
as similarity or contrast of colour, and geometrical shapes, dominated over
semantic features.
   To explain the quasi-absence of chunks from verbal protocols, de Groot
and Gobet propose a twofold explanation. First, these units are so self-
evident for masters that their access becomes automatic and unconscious.
Second, masters may not always have verbal labels associated with these
perceptual units. (The question of the use of verbal labels and of notational
systems will be taken up in Chapter 10.)


Evidence for chunks in other board games
Reitman (1976) applied Chase and Simon’s methodology combining a copy
and a recall task to Go, and studied one master and one beginner in detail.
She found that, in the copy task, there was a longer latency between the
placements of two stones with two glances at the stimulus than for those
stones placed in sequence without looking again at the model. Unlike Chase
and Simon, Reitman found a poor correspondence between the chunks
defined using the glances in the copy task and those defined with the inter-
piece latency in the recall task. A partitioning task was also carried out six
months later. The results suggest that the master saw the position as over-
lapping clusters, and not as a hierarchy of chunks as Chase and Simon
proposed with chessplayers. As we have just seen, Chi (1978), using the par-
                                            Perception and categorization    63
titioning technique, found overlapping clusters with chessplayers as well.
Altogether, these results suggest that the method used by Chase and Simon to
identify chunks is sufficient to pinpoint statistical regularities in players’
chunks, but may not be sensitive enough to identify precisely what chunks
players use.
   Similar results were obtained in a recall experiment with Othello: expert
players were superior to nonplayers at recalling meaningful game configur-
ations (Wolff, Mitchell, & Frey, 1984). Like in Go, certain game-specific
chunking procedures emerge. Wolff et al. (1984, p. 14) note that experts and
nonplayers employ different response strategies, stating that ‘7 of the 8 non-
players and 2 of the 6 experts copied the original board on a simple row-
by-row or column-by-column basis’. The other nonplayer and the four
remaining experts made a distinction between the edges of the board and the
centre. The edges were filled first and the remainder of the board was then
reproduced column-by-column (or row-by-row). According to Wolff et al.,
the edge patterns have Othello-specific clusters, while other parts of the
board, and in particular the centre, are highly volatile. This volatility may
defy strategies based on perceptual chunking, since patterns in the centre
areas are not meaningful or Othello specific.
   With awele, the least volatile of all mancala games, Retschitzki, Keller, and
Loesch-Berger (1984) tested 38 subjects (boys aged 9 to 15) on different
memory tasks, either general or in close relationship with the game. They
found a skill effect for awele material. Based on these and other results (see
Chapter 5), they concluded that the better performances came from a per-
ceptual ability that allows a quicker encoding of the patterns and makes it
easier to process the kind of information useful for playing the game.
   In the game of bao, the most volatile mancala game according to
Townshend (1986) and de Voogt (1995), no skill effect was found in de
Groot’s memory task, even with a presentation of 60 s (de Voogt, 1995; see
Chapter 5). In line with the results on Othello, volatility of bao positions
provides an explanation for this result. A comparison of bao with chess
from a computational point of view shows that chess is more complicated.
However, the changes during a move in bao bring about a much higher
volatility or mutational complexity (see de Voogt, 1995, and Chapter 2)
relative to chess. In any case, it is unclear what information gets chunked in
bao in memory tasks.


Perception in Go and gomoku
Eisenstadt and Kareev (1975, 1977) and Kareev (1973) were interested in the
role of perception and internal representations in two perceptually similar
games having different rules (Go and gomoku). Eight participants, who
could play a simplified version of both games (9×9 board), participated in the
experiment. An ambiguous position was created, which could have been
reached either in a Go or a gomoku game. Half the participants were told
64   Moves in mind
that the position was taken from a Go game, and the other half were told that
it was taken from a gomoku game. Players had to analyse the position,
then carry out an intervening task, and then reconstruct the position (without
advance warning). After solving a ‘dummy’ problem, the players received a
transformed position, which was obtained by rotating the original position
counterclockwise by 90°, reflecting it across the vertical axis, and reversing
the colour of the pieces. The participants were told that the position was
taken from the game they had not used in the first part of the experiment,
and were asked to find a good move. Again, they had a surprise recall after an
intervening task. Results showed a clear interaction, where players solving
the Go problems recalled more pieces crucial to the Go analysis than to the
gomoku analysis, and vice versa. Eisenstadt and Kareev took this result as
clear evidence that the context affects perception and memory.


Some criticisms of the concept of perceptual chunks
Chase and Simon’s method for defining chunks has been criticized by several
authors (Freyhoff et al., 1992; Gold & Opwis, 1992; Holding, 1985; Reitman,
1976), for a number of reasons. The most important of them are: (a) difficulty
in identifying chunks using reaction times, (b) impossibility of capturing
overlapping or nested chunks, (c) difficulty in dealing with pieces incorrectly
replaced, and (d) lack of support for the assumption that each chunk is
replaced in a single burst of activity during the reconstruction of the board.
Gobet and Simon (1998a, p. 229) concede that ‘these objections raise serious
difficulties if the goal is to cut a chess position into precise chunks’ but also
note that they ‘are not fundamental for analyses that relate chunks to the
distributions of relations between pieces’, as was the case in Chase and
Simon’s (1973a) study and its replication by Gobet and Simon (1998a).
Moreover, as we have seen above, the original results of Chase and Simon
have been corroborated by converging evidence from alternative techniques,
such as partitioning and sorting.
  Gobet and Simon identified two other methodological concerns. The
first was that, in recall experiments, latencies generally grow longer as items
are recalled, with the consequence that constant latency criteria may not
provide unambiguous chunk boundaries. This could explain the fact that
chunks placed early on have a larger average size than chunks placed later on:
successive pieces placed early in recall would be counted as a single chunk,
while those placed later would be counted as distinct chunks, due to their
longer latencies.
  The second concern was that subjects in the Chase and Simon study
replaced pieces by picking up several of them simultaneously. This would
have two consequences. First, subjects might have grasped pieces in a hap-
hazard fashion, and only then looked for suitable locations for them. Second,
the estimated size of chunks may have been underestimated, because hand
capacity might have restricted the number of pieces that can be grasped.
                                            Perception and categorization   65
   A difference between the original Chase and Simon’s experiments and their
replication by Gobet and Simon (1998a) was that the latter presented stimuli
with a computer instead of a physical board and pieces. They found that
masters used chunks much larger than proposed by Chase and Simon. In a
within-subject study, Gobet and Clarkson (in press) carried out the recall and
copy task both with computer display and with a physical board. They found
that masters replaced larger chunks with the computer display than with
the physical-board presentation. Thus, it seems that the characteristics of the
physical-board condition may have led to an underestimation of the size of
chunks. The fact that masters replaced large chunks in Gobet and Simon
(1998a) dovetails well with the predictions of the template theory and with
evidence brought by protocol analysis and categorization experiments that
strong players use high-level knowledge structures. We briefly review some of
the relevant evidence next (this topic will be elaborated in Chapter 5).

Recognizing high-level schemata
While there is strong empirical evidence for perceptual chunks in board
games, there is also much empirical support for the presence of high-level
knowledge structures, such as schemata. Gruber and Ziegler (1990) studied
the criteria that chessplayers, ranging from average club players to grand-
masters, used when sorting positions. They found that all players employed
knowledge units similar to the chunks identified by Chase and Simon (1973a,
1973b), but that the number of these units decreased and their size increased
with increasing expertise. In addition, stronger players used more overlapping
sorting criteria that grouped chunks together.
  A number of investigators (Gruber, 1991; Jongman, 1968; Nievergelt,
1977) carried out ‘guessing experiments’, where players had to find the
locations of all pieces in an as yet unseen position. To do so, they could ask
whatever questions they deemed adequate, and received a ‘Yes’ or ‘No’
answer. Results showed that chess experts tended to ask about the past and
future path of the game, about plans and evaluations, and so on, while
novices enquired about the locations of single pieces. (See also Binet,
1894, and de Groot, 1946, for early investigations on the role of complex
knowledge in chess; a detailed rendition of Jongman’s (1968) work can be
found in de Groot and Gobet (1996).)


Concepts in Go
The game of Go uses a rich terminology of concepts, which cover various
aspects of the game (Shirayanagi, 1986). For example, common concepts are
‘kosumi’ (a diagonal extension) or ‘shinogi’ (saving an endangered group
of stones). Yoshikawa et al. (1999) were interested in the way Go players use
such concepts. When facing a new position, strong players show a behaviour
similar to the ‘first phase’ observed by de Groot (1946) with chessplayers:
66   Moves in mind
they first evaluate their own and their opponent’s possibilities globally, using
concepts, and, only in a second stage, generate candidate moves and look
ahead. The use of concepts varies as a function of skill. Novices, who know
few of the standard names for concepts, create their own terms. Intermediate
players can recognize when concepts apply in a position. Unlike advanced
players, they lack associations that interconnect concepts and link them with
evaluations or plans. According to Yoshikawa, Kojima, and Saito, knowledge
of terms is only the tip of a master’s iceberg of perceptual and conceptual
knowledge, a view that is consistent with the chunking and template theories.


Conclusion
Along with the anecdotal evidence about the skill displayed by grandmasters
like Kasparov or Sijbrands, the empirical evidence reviewed in this chapter
strongly supports the role of perceptual chunking in board games. That to
which players pay attention leads to the acquisition of perceptual chunks,
which, in turn, directs attention to the relevant features of the situation at
hand. Evidence for these mechanisms was provided both by eye-movement
studies and by the good memory for briefly presented positions. The only
exception was bao, where no skill effect was found in a memory task (see
Chapters 5 and 10).
   Among the theories we have reviewed in the preceding chapter, only the
chunking theory, the template theory, and Saariluoma’s theory directly
addressed perceptual chunking in some detail. While they differ about the
details, all three agree that chunks play a key role in perception, and in
cognition in general. The chunking and template theories both led to com-
putational models simulating chessplayers’ eye movements—respectively
PERCEIVER (Simon & Barenfeld, 1969; see Chapter 6) and CHREST (de
Groot & Gobet, 1996). CHREST was able to account for the detail of eye
movements, using, among others, mechanisms that directly depend on the type
and number of chunks acquired. Overall, the strong support for the existence
of chunks must count against Holding’s SEEK theory. This is because
Holding (1985, 1992) explicitly denies the reality of perceptual chunks.
   At first blush, Saariluoma’s (1984) results about attack detection and
piece identification seem inconsistent with chunking mechanisms. This
evaluation does not stand up to a more rigorous analysis, however. Chunking
mechanisms can explain the skill effect in deciding whether one piece attacks
another, because there are only a limited number of cases where this could
occur. Given masters’ extensive practice, these cases could have been learnt
as constellations of pieces in memory, as postulated by the chunking theory.
In order to account for masters’ ability to identify pieces rapidly, one has
to postulate learning at a different grain size. The EPAM theory, which is at
the basis of the chunking and template theories, can account for learning at
both levels (Richman, Gobet, Staszewski, & Simon, 1996). EPAM acquires a
large network of tests to discriminate among different stimuli. For example,
                                            Perception and categorization   67
it has been used to learn to recognize letters by distinguishing the lines
that compose them, and to recognize words by distinguishing their letters
(Richman & Simon, 1989). In a similar fashion, CHREST can discriminate
chess pieces by learning their distinct features, in addition to learning the
arrangements of pieces that compose patterns on the board.
   The chunking and template theories give a detailed account of the pattern
of chess relations found within, but not between, chunks. One could argue
that the simulations carried out by MAPP (Simon & Gilmartin, 1973) used
chunks selected by the programmers, but this criticism is not valid with
CHREST. Gobet (2001b) describes how this model, which acquires chunks
and templates automatically by scanning a database of master games, learns
chunks that closely reproduce the pattern of relations found in the human
data.
   Taken together, the results we have reviewed support the concept of chunks
and the estimate that it takes at least 2 s to access a new chunk. There is
also evidence indicating that strong players use higher level types of descrip-
tions. This evidence, often taken as a weakness of the chunking theory
(e.g., Cooke et al., 1993; Holding, 1985), turns out to be one of the strengths
of the template theory. This theory was developed precisely to account for
these phenomena and hence contains mechanisms for acquiring high-level
knowledge. It explicitly proposes that experts encode knowledge as relations
between chunks and store other information besides the locations of pieces.
Evidence for high-level knowledge will also be a recurring theme in the
following chapter, devoted to memory.
5      Memory, knowledge,
       and representations




Research into expertise in general and board games in particular has been
dominated by studies of memory. There are three reasons for this state of
affairs. First, memory has traditionally been a popular topic for scientific
psychology. Second, it is easier, both conceptually and practically, to
carry out experiments on memory than, say, perception or problem solving.
And, finally, Chase and Simon’s series of papers on chess memory,
which have had such an impact on research into expertise (Charness,
1992), also had a direct influence on the type of methodology used. In
spite of this emphasis on memory, most researchers’ ultimate goal is still
to understand expertise in general; hence, links with perception, problem
solving, and decision making are apparent in the works reviewed in this
chapter.
   We now have a clear picture of what kind of variables matter in board-
game memory. The main findings will be discussed in the following sections,
but it may be useful to give a preview of the main results. Even with presenta-
tion times of 1 s, chess masters recall whole positions with high accuracy;
randomizing positions significantly lowers the performance of experts,
who still perform slightly better than weaker players; and the skill effect
uncovered by de Groot in chess—experts recall domain material better
than nonexperts—has been found with most board games and in a number of
alternative domains, including card games (bridge: Charness, 1979; Engle &
Bukstel, 1978; skat: Knopf, Preussler, & Stefanek, 1995), electronics (Egan
& Schwarz, 1979), sports (Allard, Graham, & Paarsalu, 1980; Allard &
Starkes, 1980), and computer programming (Schneiderman, 1976).
   Since Chase and Simon’s research, the memory recall paradigm has been
subjected to many variations. Most of the experiments have been motivated
by Chase and Simon’s chunking theory, which thus offers a natural frame-
work for organizing the material. We now consider how several variables
affect memory for board-game positions, starting with game positions. In
the conclusion of this chapter, we discuss how the empirical data relate to the
main theories of expertise in board games.
70   Moves in mind
Memory for board positions

The standard experiment: Memory for game positions
As we have seen in Chapter 3, Djakow et al. (1927) took advantage of the
1925 Moscow tournament to subject 12 of the best chessplayers of the
time to several psychological tests. One of these tests became ‘the’ classical
task in the study of experts’ memory: the experimenter briefly presents
domain-specific material (e.g., a chess position) and then takes it out of sight
of the participant, who has to reconstruct this material from memory. While
Djakow et al. found that masters were slightly better than nonplayers,
the skill difference was obscured by two features of their methodology: a
relatively long presentation time (60 s) and a nontypical chess position (an
artistic chess problem). The task was later refined by de Groot (1946), who
employed faster presentation times (from 2 to 15 s) and used positions taken
from masters’ games (see Figure 5.1, left). De Groot’s results were clear cut:
his grandmaster and master obtained a recall percentage close to 100%
correct, while his weaker players, relatively good amateurs, barely reached
50%. It has later been shown that complete novices can hardly remember
more than three pieces, about 12% (Chase & Simon, 1973a, 1973b; Gobet &
Clarkson, in press). A third methodological innovation—the use of random
positions— was made by two of de Groot’s students, Lemmens and Jongman
(unpublished study mentioned in Jongman, 1968, p. 57) and later fully
explored by Chase and Simon (1973a, 1973b). With random positions,
masters’ performance drops and their superiority over novices all but
disappears (see next section).
   The skill effect with meaningful positions has also been found in other
board games, such as Go (Eisenstadt & Kareev, 1975; Masunaga & Horn,




Figure 5.1 Types of position used in chess research on memory. On the left, a game
           position taken from a tournament game. On the right, a random position
           obtained by shuffling the piece locations of a game position.
                                  Memory, knowledge, and representations       71
2000; Reitman, 1976), gomoku (Eisenstadt & Kareev, 1975), Othello (Wolff
et al. 1984), and awele (Retschitzki, 1990). In some cases, such as Go, a
simplified version of the game was used; for example, Masunaga and Horn
(2000) used an 11×11 grid and from 12 to 16 stones.
   Experts’ scores tend to be lower with these games than with chess, which
can partly be explained by the volatility of the positions in these games
and the total number of pieces to recall. Thus, these results suggest that the
near perfect scores of chess masters on meaningful positions cannot be
generalized to all board games. When used, control tasks unrelated to the
board game under study indicate that the skill effect in memory recall does
not transfer to other domains (Masunaga & Horn, 2000; Retschitzki, 1990).
   De Voogt (1995) conducted a pilot study on bao experts to investigate
the possibility of using de Groot’s recall experiment. One of the most co-
operative and motivated players was asked to reproduce a meaningful bao
position after studying it briefly. After several trials and needing at least 30 s,
he was not able to reproduce the position with great accuracy; indeed, he did
not perform better than the researcher. De Voogt concluded that this task
appeared alien to the bao expert and was not useful to distinguish expert and
novice in the game.
   Bao positions are more volatile than positions in chess or any other game
that has been subject to psychological investigation. Even within the
mancala games family, games with similar spreads of counters, it is the game
with the most dynamic or volatile positions. From this comparison, one
can understand why the attempt to use de Groot’s recall task with bao was
unsuccessful. The recognition or recall of bao positions is a skill of little use
to bao masters since the entire position is considered volatile and hardly
suitable for meaningful position patterns. As we shall see below, additional
experiments in bao showed that performance on recall of move sequences may
distinguish experts from novices, rather than performance on recall of board
positions.
   This exception will be further discussed in the conclusion of this chapter.
Thus, although the available results about board-game memory confirm a
significant skill effect for most games, the nature of the game may affect the
level of performance on memory recall experiments.


Random positions
Experiments on the recall of random positions (see Figure 5.1, right) are
theoretically interesting, given that this type of material controls for meaning.
Memory for meaningful positions can always be explained in a number of
ways (e.g., chunks, schemas, retrieval structures), but it is harder to account
for memory performance with random material. Here, the theorist navigates
the narrow path (a few percentage points) between the Scylla of predicting
too much recall, and the Charybdis of not predicting enough recall.
Experiments with short presentation times are discussed in this section; those
72   Moves in mind
with long presentation times are discussed in the section on the role of
presentation time on memory recall.
   Chase and Simon (1973a, 1973b), who used a presentation time of 5 s, did
not find any recall difference between their three subjects (a master, a class A
player and a beginner) with random positions. This result, supported by
unpublished data by Jongman and Lemmens cited in Jongman (1968),
has become a ‘classic’ in cognitive psychology, to be found in most text-
books. Contrasting with these results, simulations with CHREST showed
that the chunking and template theories actually predict a small, but reliable
superiority for experts (Gobet, 1998c; Gobet & Simon, 1996a, 1996b, 2000a).
The reason is that a large storehouse of chunks makes it more likely that
chunks will be recognized serendipitously in random positions. This led
Gobet and Simon (1996b) to comb the literature in search of experiments
where random positions were used with a rapid presentation time (less or
equal to 10 s). They found a dozen of such studies; as predicted by CHREST,
there was an overall correlation between skill level and recall performance,
although it was rarely statistically significant in the individual studies. The
lack of statistical power of most experiments explains this situation: the
sample size is typically small, as is the effect size (with a presentation time of
5 s, even masters do not place more than an average of 5.5 pieces correct with
random positions). When samples are larger, the effect becomes reliable
(Gobet & Waters, in press; Gold & Opwis, 1992).
   Several studies have explored how various types of randomization affects
recall (additional studies will be dealt with in the section about the number
of chunks in LTM). Based on de Groot’s (1946) protocols, Reynolds (1982)
suggests that weak players focus on piece location, while stronger players
direct their attention to the functional distribution of important squares,
which are often located at the centre of the board. To test this hypothesis,
Reynolds varied the extent to which pieces impinged on the centre. There was
a skill effect only for positions in which piece influence was directed toward
the centre.
   Vicente and Wang (1998) note that the random positions used in chess
research are not really random, as they still contain information about
the distribution of pieces in master games (e.g., only one white and black
King, almost never more than two white Knights, no more than eight
white Pawns). They propose a new type of random position (‘truly random
positions’), where both the location and the distribution of pieces are
randomized. They also state that their constraint-attunement hypothesis
(see Chapter 3), which has been applied to explain expert recall in a number
of domains, predicts no skill effect with such positions, while the chunking
and template theories do. Gobet and Waters (in press) carried out an
experiment to test these predictions. There was a statistically significant
skill effect with truly random positions, which is consistent with the chunking
and template theories, but inconsistent with the constraint-attunement
hypothesis.
                                 Memory, knowledge, and representations      73
   Overall, the results with other board games show a pattern consistent
with chess: a trend towards a skill effect with random positions, but non-
significant results due to a lack of statistical power. With Go, Reitman’s
(1976) master (ranked 4-dan) scored 66% in a meaningful position, and her
novice 39%. In random positions, the scores were 30% and 25%, respectively.
(See Figure 5.2 for examples of the positions used by Reitman.) The scores
with game positions are lower than for chess, and the differences between
game and random positions do not appear statistically significant. The
different nature of Go chunks, as well as the fact that only two subjects took
part in the experiment, may account for this pattern of results.
   Wolff et al. (1984) studied six skilled Othello players (from class A players
to Experts), and compared their results with eight students who had never
played the game. They used a presentation time of 12 s and positions with
47 pieces. They found a significant interaction between skill level and type of
position. Experts scored 63% correct with meaningful positions, and non-
players 44%. Wolff et al. explained experts’ relatively poor recall performance
by the volatility of the position in Othello, which leaves a large part of the
position without meaning. With random positions, the scores were 38% and
32%, respectively, a difference which was not statistically reliable.


Role of presentation time
Presentation time is an interesting variable to manipulate, as it is likely to
provide useful information about the time cost associated with memory
mechanisms (e.g., storage and retrieval). This variable may also be infor-
mative about learning rates. Starting from the hypothesis that patterns stored
in LTM are not equally familiar, Chase and Simon (1973b) speculated about
the time course of the cognitive mechanisms involved in chunk identification.
They proposed that two mechanisms operate during the initial perception of
a position. At the beginning, players perceive familiar chunks; later, attention
switches to less familiar chunks or to isolated pieces, and new chunks
may be learnt. In other words, the probability of encoding a chunk is high
in the early stage of perception and the probability of encoding isolated
pieces is high in the later stages. Combined with the fact that, although a
piece may belong to several chunks, it will be replaced only once, Chase
and Simon’s mechanisms predict that later chunks will be smaller, and, as a
consequence, the rate of memory improvement will decrease as presentation
time increases.
   Let us consider the results with game positions first. Several studies
(Charness, 1981c; Gobet & Simon, 2000a; Saariluoma, 1984) support Chase
and Simon’s hypothesis. In Gobet and Simon’s experiment, which provides
the most complete set of data, the sample included players ranging from
weak amateurs to professional grandmasters, and the presentation time
was systematically varied from 1 s to 60 s. As can be seen in Figure 5.3, the
rate of information intake diminishes as the presentation time increases. Like
74   Moves in mind




Figure 5.2 Examples of the Go positions used by Reitman (1976). Top, meaningful
           pattern; bottom, random pattern. (After Reitman, 1976.)


a variety of learning and memory data (Lewis, 1960), Gobet and Simon’s
data can be fitted with a logistic growth function, as can also be seen in the
figure. Note that masters recall whole positions almost perfectly, even with
presentation times as short as 1 or 2 s.
                                   Memory, knowledge, and representations        75




Figure 5.3 Percentage of pieces correct as a function of presentation time and chess
           skill for game positions (top panel) and random positions (bottom panel).
           The figure also shows the best fitting exponential growth function for each
           skill level. (After Gobet & Simon, 2000a.)


  Analysis of the parameters of the logistic growth function suggests two
differences due to skill: first, stronger players memorize more with a very
brief presentation time; second, they improve their score faster with longer
presentation times. These results are consistent with the emphasis of Chase
76   Moves in mind
and Simon’s chunking theory on recognition processes, but also suggest that
skilled players are more efficient in the second stage. Two complementary
explanations can account for the latter skill effect: strong players recognize
more chunks with additional time, and they learn new chunks faster, since
they can use larger chunks as building blocks for further learning. These
results are partly reflected by the size of chunks. Even after a 1-s view of the
board, masters reconstruct large chunks (up to 13 pieces); the size of their
largest chunk increases only slightly with additional presentation time (up to
17 pieces). Experts and class A players start with smaller chunks, which also
show an increase in size with additional presentation time.
   Lories (1987a) showed that there is a skill effect with random positions
when they are presented for one minute, but did not give any information
about the learning curve. As with game positions, Gobet and Simon (2000a)
varied the presentation from 1 to 60 s, and, again, found that an exponential
growth function provided an excellent fit to the data (see Figure 5.3). The
pattern of results was the same as with game positions, with the obvious
difference that the percentage of recall was lower with random positions.
Players of different skills varied in how much they were able to memorize
after a very short exposure; they also varied in the rate with which they
improved with additional presentation time. In both cases, masters showed
a slight, but reliable, superiority over weaker players. As predicted, all skill
levels increase the size of their largest chunks with additional presentation
time (from five pieces with 1 s to more than 10 pieces with 60 s for masters).
Finally, the task is challenging even for masters, who, with a 1-minute
exposure, can replace correctly only about 17 out of 26 pieces (68%), on
average.
   The experiments we have described so far used a visual presentation. How
does presentation time affect performance with an auditory presentation,
where players presumably recode verbal information into a visuo-spatial
format? Saariluoma (1989) addressed these questions by dictating positions,
one piece every 2 or 4 s (a total presentation time of 50 and 100 s for the
entire position, respectively). As with visual presentation, results show
that strong players are better in the recall of both game and random
positions, and that the performance of all players increases with longer
presentation times. Saariluoma also found that strong players maintained
their superiority when the task was to memorize four game positions
simultaneously, but that players of all skill levels performed poorly with four
random positions.


Interference studies
Chase and Simon’s (1973b) theory postulated a limited-capacity STM, with
relatively slow LTM encoding. Empirical research has uncovered several
weaknesses with these aspects of their theory. Consider the case of the classic
de Groot recall experiment, with a short presentation time of 5 s. Chase and
                                 Memory, knowledge, and representations      77
Simon’s theory proposes that information is temporarily stored in STM, and,
since the presentation is rapid, there is not sufficient time for LTM encoding.
Therefore, it clearly predicts that storage of additional stimuli following the
chess position should wipe it out from STM. Several experiments show that
this is not the case.
   It had been known since de Groot (1946) that the insertion of a delay
between the presentation of the position and its recall does not affect per-
formance. De Groot (1946/1978, p. 323) actually recommended that his
subjects wait for about 30 s before reconstructing the position—an interval
supposed to allow them to ‘organize whatever they could retain’. Chase and
Simon (1973b) directly tested the effect of a waiting period with one of their
subjects, and did not find any decrease in recall performance in comparison
with immediate recall. Charness (1976) obtained similar results, and the
presence or absence of instructions to rehearse did not matter much (about
8% deficit in the nonrehearsal condition). Similarly, when de Voogt (1995)
asked a bao master to reconstruct a move, waiting times for up to 3 minutes
did not result in any decrease in recall performance. But what happens when
the waiting period includes an interfering task—a direct test of the chunking
theory? Several chess experiments have addressed this question. With a
delay of 30 s between the presentation and the recall of a position, filled by a
task such as counting backwards, Charness (1976) found that players took
longer than in the standard condition to replace the first piece. The overall
loss in performance was only 6 to 8%—little in comparison with experiments
where subjects had to recall verbal material (e.g., nonsense trigrams).
Surprisingly, inserting an interference task related to chess (such as finding
the best move or naming the pieces in another board) did not produce a
significant drop in recall percentage either. These results suggest that at least
part of the information gets encoded into LTM rapidly.
   Frey and Adesman (1976) reached a similar conclusion. They presented
two positions for 8 s each to their subjects, who had then to count backward
and aloud for 3 or 30 s. Finally, subjects had to reconstruct the first or the
second position, without knowing in advance which one would be chosen. As
with Charness, the manipulation produced only a small loss of performance,
when compared to a control condition where only one board was presented.
A natural extension of this experiment is to ask subjects to reconstruct both
positions, or even to memorize a longer sequence of positions. Cooke et al.
(1993) presented up to nine positions (shown for 8 s each), and Gobet and
Simon (1996c) presented up to five positions (shown for 5 s each). The results
were consistent across both studies: increasing the number of boards pro-
duced a decrease in percentage correct, but an increase in the number of
pieces recalled correctly. There seems to be a limit in the number of boards
that can be recalled with some accuracy (above 60% correct)—around four
or five. This limit may be overcome by the use of special mnemonics. One
subject in the 1993 study by Cooke et al. (partially) recalled seven boards
out of nine, and seems to have used a mnemonic in which each board was
78   Moves in mind
associated with the name of a famous player. Based on this study, Gobet and
Simon (1996c) trained a master to apply a similar technique; he was able to
memorize, with accuracy higher than 70%, up to nine positions presented for
8 s each, replacing as many as 160 pieces correctly.
   De Voogt (1995) also asked a bao master to reconstruct a sequence of
board positions, and found that the limit was at three boards, with a clear
decrease in performance. Although reconstruction in this case consisted in
returning a move from a set position, as explained later in this chapter, this
result seems consistent with what was found in chess.
   There is little evidence about the role of interfering tasks with other board
games. In their comparison of Go and gomoku, Eisenstadt and Kareev
(1977, p. 550) asked their subjects to analyse a game, perform an inter-
vening task, and, then, without advance warning, reconstruct the original
position from memory. Unfortunately, they did not evaluate the effect of
the intervening task, as they were mainly interested in the effect of prior
knowledge on the reconstruction of Go and gomoku positions.


Number of pieces
Experiments varying the number of pieces in the position tell us something
about memory limitations and encoding mechanisms, on the one hand,
and the role of typicality, on the other. In particular, they may shed light on
the nature of the chunking theory’s parameters. In one of their experiments,
Chase and Simon (1973a) studied the difference in the recall of endgame
positions, where few pieces are left (average number of pieces = 13), and
middlegame positions (average number of pieces = 25). They found that,
other things being equal, their master and class A player retained more
pieces in the middlegame positions than in the endgame positions. The
hypothesis of a ceiling effect may be ruled out, since their master recalled
only about 8 pieces in the endgame positions. This result has been replicated
by Saariluoma (1984), who presented positions containing 5, 15, 20 and
25 pieces. Saariluoma used the chunking theory to explain these data.
Strong players can recognize various constellations in opening and early
middlegame positions, which tend to be typical. By contrast, they cannot
do so in endgame positions, which are less predictable and thus harder to
code as chunks. Typicality, rather than the number of pieces, seems to matter
in these experiments. To our knowledge, no one has carried out an experi-
ment in which the size of the input was varied while keeping typicality
constant.
  Not much is known about this question for other board games. Reitman
(1976), in her study of a Go expert and novice, used stimulus patterns of 22–25
and 12–15 stones in the recall tasks. Unfortunately, this distinction of number
of pieces was not analysed, and it is therefore not clear what the effect of
number of pieces on Go players’ performance is.
                                 Memory, knowledge, and representations     79
Recognition experiments
So far, we have dealt with tasks where players have to recall board-game
positions. Another common technique in memory research—although not so
much in board-game research—is the recognition task, where participants are
first shown a sequence of stimuli, and then a second sequence, of which they
have to decide whether they have previously seen the items. New items act as
distractors.
   There is a skill effect when game positions are used in recognition tasks,
both with short and long presentation times (Goldin, 1978a, 1978b, 1979;
Saariluoma, 1984). Moreover, typical positions are better recognized
(Goldin, 1978b). Finally, deep processing of the material, such as choosing a
good move or evaluating the position, facilitates recognition in comparison
to a superficial treatment, such as counting the number of pieces on black
squares or copying the position (Goldin, 1978a). Interestingly, recognition
performance is relatively high even with tasks that do not require deep pro-
cessing (more than 70% for class A players). According to Goldin, these
results support Chase and Simon’s (1973a, 1973b) emphasis on perceptual
processes, and suggest that pattern recognition mechanisms are rapid,
automatic, and hard to inhibit.
   The skill effect with game positions extends to the recognition of random
positions. Indeed, there is no robust decrease in performance in comparison
to game positions: Saariluoma (1984) found a decrease of 10%, but Goldin
(1979) found that recognition was slightly better (2%) with scrambled
positions. The length of presentation time (50 s with Goldin, 1979, and 8 s
with Saariluoma, 1984) did not affect this result. Goldin suggests that players
can use their chess knowledge to encode some of the meaningful patterns that
occur even in random positions. Given that the task simply requires one to
discriminate between old and new items, this strategy is sufficient to explain
the skill effect. Lories (1984) proposes a similar mechanism for strong players,
and notes that the relatively long presentation time used in these experiments
facilitates the encoding of retrieval cues. According to him, weaker players
use a similar strategy, but, given their lack of chess knowledge, have to con-
tent themselves with less efficient types of information, such as geometrical
regularities. Saariluoma (1984) has adduced direct experimental evidence
in favour of the role of chess patterns in recognition experiments: when the
spatial relations between the pieces are destroyed by deleting all empty
squares (all pieces are put beside one another), the skill effect disappears.
   McGregor and Howes (2002) asked participants to evaluate a chess
position, presented for either 9 or 30 s; a recognition test was later per-
formed. One experiment studied two methods of distorting positions
during recognition, either by shifting all pieces or a single piece one square
horizontally. In two other experiments, a priming methodology was used
during recognition. A piece from the target position was shown for two
seconds; then, a second piece was shown, and participants had to decide
80   Moves in mind
whether it was present or not on the board. The relation between the two
pieces was either one of attack/defence or proximity. The results of these
experiments showed that class A players made more use of attack/defence
relations than of the location of pieces.
   With other board games, we were able to find only one instance of the use
of the recognition paradigm. In the multitask Go study we have already
mentioned, Masunaga and Horn (2000) measured short-term recognition
under distraction. Meaningful Go configurations (from 13 to 37 stones) were
presented for 7 or 11 s. Players had to count the number of black and white
(or, black or white) stones, and memorize the position. After the position had
been taken away, players wrote down the outcome of their counting, and
selected the presented position from a choice of six configurations. Results
indicated a monotonic decrease in performance between the four skill levels
under study (professional, advanced, intermediate, beginner), with a clear
difference between professionals and the other players. No skill effect was
found in a control task tapping the same cognitive processes.


Guessing experiments
Our review of experiments on memory for positions indicates that, in most
cases, board-game experts do perform well. Can we explain these results by
players’ knowledge of what is ‘typical’ in a given board game? This is the
question that de Groot and Jongman (de Groot, 1966; de Groot & Gobet,
1996; Jongman, 1968) addressed in a series of chess experiments, the logic
of which was to estimate how much of a position could be constructed
correctly without having seen the position beforehand. A first approach was
to create a stereotypical position, based on the frequency of piece locations in
192 games (see Figure 5.4). When this position was used as a best guess in a
set of independent positions, the average percentage of correct placements
was 45% (more than the performance of the weak players, who obtained 37%
correct on average). A second approach was to ask players to guess the piece
location in an unknown position. Unlike in the technique discussed in the
previous chapter, players do not ask questions, but simply place pieces on the
board. After each trial, the incorrect pieces are removed, and the player tries
to guess the position again. Compared with a memory task where players
are similarly given several trials, the results show that masters obtain as
many correct placements when they guess the position as weak players in the
memory condition. In both cases, there is a rapid increase from the first trial
(about 38%) to the second trial (about 60%), followed by smaller increments
up to 95% correct after 12 trials. In addition, while masters do substantially
better in the memory condition than in the guessing condition, there is no
such difference between the conditions for weak players. The results of the
guessing condition suggest that masters are able to use the location of a few
pieces to categorize the position or aspects of the position, which enables
them to infer the location of other pieces.
                                 Memory, knowledge, and representations     81




Figure 5.4 De Groot’s (1966) stereotyped position, based upon 192 games after
           black’s 20th move.


  In a similar task, Chase and Simon (1973b) asked chessplayers to guess a
position where the pieces were replaced by pennies. Given these cues, a master
performed almost perfectly, and a class A player obtained a performance
higher than 90%. Again, the results indicate that players can use partial cues
to help categorize the position. We will return to de Groot and Jongman’s
guessing experiment and Chase and Simon’s penny-guessing task in the next
section, when discussing memory for Go moves.


Recall of sequences of moves and of games

Chess
The recall task has also been used with sequences of moves. Chase and Simon
(1973b) found a correlation between skill level and recall percentage, even for
sequences of random moves, although all players were slower to reproduce
random moves. According to Chase and Simon, the rather long exposure
time (about 2 minutes in total) accounted for this skill effect for random move
sequences. This time was sufficient for the material to be reorganized and
encoded into LTM permanently. Finally, based on the analysis of errors and
length of pauses, Chase and Simon hypothesized that sequences of moves
were organized hierarchically around a goal. This conjecture was supported
by Gruber and Ziegler (1993), who asked players to partition entire games,
and also analysed verbal protocols of planning behaviour.
   Saariluoma (1991) tackled the question of memory for move sequences
82   Moves in mind
using blindfold chess. In this variety of chess, first studied by Binet (see
Chapter 3), a player carries out one (or several) game(s) without seeing the
board and the pieces; the moves are indicated using standard chess notation
or displayed on a computer screen. Saariluoma dictated moves at a brisk
pace (one piece moved every 2 s), from three types of games: one game
actually played, one game where the moves were random but legal, and one
game where the moves were random and possibly illegal. After 15 moves,
Saariluoma’s masters had almost perfect memory of the position for the
actual game and legal random games, but could not recall more than
20% with the random illegal games. The novices did worse in all three
conditions.
   Saariluoma (1991) advanced the following explanation, based on the
chunking theory. He first assumed that the presentation time was long
enough for players to associate chunks with information about moves. With
games, strong players were better because they could use their large store-
house of chunks. With random legal games, they were still more likely to find
chunks than weaker players. With random illegal games, however, it became
much harder for masters to find chunks, and their performance dropped.
Phrased differently, random legal games drifted only slowly into positions
with few opportunities to recognize chunks; hence, they initially allowed for a
relatively good recall. The further away from the starting position, the harder
recall became—the recall with legal random games dropped to 60% after 25
moves, while the recall of actual games stayed around 90%. Finally, random
illegal games drifted more rapidly into chaotic positions, where hardly any
chunk could be recognized and recall was therefore low.


Go
Earlier in this chapter, we described two experiments where participants
had (partly) to guess the location of pieces on the chessboard: de Groot and
Jongman’s guessing task and Chase and Simon’s penny-guessing task.
Recently, Burmeister adapted these experimental techniques for studying
memory of moves in Go (Burmeister, 2000; Burmeister, Saito, Yoshikawa,
& Wiles, 2000; Burmeister, Wiles, & Purchase, 1999). The modification of
the penny-guessing experiment included two conditions. In the memory con-
dition, a game was presented, one move every 2 s. The games were chosen so
that the position grew incrementally (i.e., there was no capture of stones).
During the test phase, players could see the final position, and had to indicate
the order with which the stones were placed on the board. The com-
puter software gave immediate feedback about incorrect placements. In the
sequential penny-guessing condition, players saw the final position, but not
the moves leading to it. They had to guess the order with which the stones
were placed. As expected, results collected with four experienced players
(between 10 and 1 kyu) and four beginners (between 25 and 15 kyu) indicated
that, for all participants, performance was better in the memory condition
                                 Memory, knowledge, and representations      83
than in the guessing condition. More surprisingly, the experienced players
performed better in the guessing condition than the beginners in the memory
condition.
   The adaptation of de Groot and Jongman’s guessing task followed similar
lines. The only difference was that the final position was not shown when
players attempted to replay the moves in the game. In the memory condition,
players saw the moves and could use their memory for reconstructing the
game; in the sequential guessing task, they had to find them. Results were
similar to the previous experiment: players did better in the memory than
in the guessing condition, and experienced players tended to be better in
the guessing condition than the weaker players in the memory condition.
Burmeister (2000) also investigated how strong players (one 8-dan and two 6-
dan players) performed in the memory condition when the presentation
time of the moves was reduced. Even with durations as short as 500 ms, the
8-dan player performed close to perfection after one trial, and the 6-dan
players obtained about 80% correct. Players’ comments indicated that they
tried to organize moves around meaningful episodes, and that they also took
advantage of ‘joseki’ and ‘tenuki’, that is, known patterns and sequences of
moves. Performance in these tasks seemed to be a function of recognition
memory, reconstruction memory, and problem solving, which dovetails with
the results obtained in chess (Chase & Simon, 1973b; de Groot & Gobet,
1996).


Other board games
Memory for moves and games has been investigated with other board games
as well. Wolff et al. (1984) read the first 20 moves of an Othello game to
skilled players and nonplayers, who had both to place the piece on the board
and complete the move (i.e., by flipping the captured pieces). After the trial,
the experts and nonplayers were asked to replay the moves. The time was
limited to 15 s per placement of a piece. None of the nonplayers gave a
perfect recall, while four out of five experts did. A statistical analysis of the
second part of the move sequence indicated that familiarity with standard
openings could not entirely explain the difference. Interestingly, the difference
between nonplayers and experts was larger in the memory-of-move task than
in the memory-of-board task. In the first case, nonplayers committed about
four times more errors; in the second case, they committed only about 1.5
times more errors. This result is in line with other findings showing that, with
experts of volatile games such as bao, memory for move sequences is more
important than memory for positions (de Voogt, 1995).
   Retschitzki (1990) asked two adult awele experts to replay exactly the same
moves of a game they had just finished. Even though these players were
instructed to try to remember exactly what they had played, they failed
to reproduce the same sequence of moves. This unique trial is insufficient to
argue that they were unable to do the task, inasmuch as the loser of the game
84   Moves in mind
was reluctant to play the same bad moves and tried to change his tactics.
(Incidentally, this failed experiment is a typical example of the type of prob-
lems facing researchers in cross-cultural settings.)
   The history of Othello shows a shift from positional to mobility strategies.
In positional games, the expert focuses on board patterns, while in mobility
games, the moves are chosen to limit the opponent’s choices and maximize
one’s own. A possible reason for the preference towards positional strategy
early on may be that this strategy leads to patterns that are more memorable.
To test the hypothesis of an intrinsic difficulty of the mobility strategy in
Othello, Billman and Shaman (1990) asked players to remember move
sequences generated randomly (but legally) and move sequences taken from
positional games and from mobility games (see Figure 5.5). Players trained
in positional strategy found mobility sequences ‘random’ and even more
difficult than random sequences, which, apparently, could partly be under-
stood through positional strategy. Their recall performance reflected this
subjective ordering of difficulty.


Undoing moves
Backing up a series of moves is difficult in most board games (Eisenstadt &
Kareev, 1975), but undoing a single move typically does not pose much
difficulty. It is trivial in chess, and may sometimes require thought in inter-
national draughts. Bao is one of the few games in which undoing a move
can become problematical for a master and can prove too complicated for
a regular player. This is due to its peculiar rules. As in other mancala
games, moves consist of a spreading of counters around the board; unlike
other games, captured counters are re-entered according to strict rules. This
may result in multiple changes of a position (there is a maximum of eight
captures), and, as a consequence, lead to difficulties in undoing a move.
De Voogt (1995) designed a recall experiment in which experts were first
presented with a position, then shown a move with its cascaded con-
sequences, and finally required to undo the move, so that they would
reconstruct the initial position (see Figure 5.6 for an example). All bao
experts performed flawlessly, while bao novices commonly did not.
  The task can be complicated if one shows only the starting position,
without the sequence of actions, and then asks the player to reconstruct the
move from the end position. Such a task is considered nearly impossible,
and only one master volunteered to do so. This master performed flawlessly
up to two games simultaneously; that is, two starting positions were shown,
sometimes followed by interpolated tasks for up to 3 minutes, and the player
had then to return to the starting positions from the end positions.
  A nonplayer asked to recall such positions consisting of a set of 16
numbers (equivalent to two rows containing seeds) could be somewhat suc-
cessful, in particular after a certain amount of practice. Yet the bao master
remembered the position through reconstruction of the move and did not
                                  Memory, knowledge, and representations       85




Figure 5.5 Othello boards after the 10th and 20th moves of a game using positional
           strategy. (After Billman & Shaman, 1990.)


perform well on a position recall task. Apparently, position chunking is not a
practised skill for bao masters, while chunking move sequences is.
  The experiment of returning moves resembles that of position recall
experiments in that positions are reproduced on the board. At the same time
86   Moves in mind




Figure 5.6 Example of the types of position used in the experiment on undoing
           moves. The description of the move leading from the position at the top
           of the figure to the position at the bottom runs over 18 lines! (After
           de Voogt, 1995.)

it may be compared to experiments in other domains in which a series of
moves is reconstructed rather than a position.


Estimation of the number of chunks in LTM
As mentioned in Chapter 4, Chase and Simon (1973a) analysed the relations
between successively placed pieces in two different tasks (a recall and a copy
task) and in two different types of chess position (game and random). They
found that successive pieces belonging to the same chunk were more likely to
                                 Memory, knowledge, and representations      87
share a high number of relations than successive pieces not belonging to a
chunk. These analyses, as well as their replication and extension by Gobet
and Simon (1998a), can be taken as support for the chunking and template
theories, which both make strong predictions about the structure of chunks.
In particular, with chess, pairs of pieces that have numerous relations (attack,
defence, proximity, same colour, and same type) are more likely to be
chunked, because they tend to be noticed together more often. We have also
seen that different experimental techniques offer converging evidence about
the psychological reality of chunks as defined either by numbers of chess
relations or latency in placement. For example, pieces presented rapidly are
better retained when they are presented in chunks than when they are pre-
sented either by columns or randomly (Charness, 1974; Frey & Adesman,
1976).
   A question that has fuelled a fair amount of research concerns how
much information must be known to develop expertise, where ‘how much’
is measured by ‘how many chunks’. Beyond chess and board games, this
question has obvious implications for instruction and training in general:
if expertise requires the acquisition of a large storehouse of chunks rather
than a few general principles, different educational methods should be used.
Based on extrapolations from the simulations performed by MAPP, Simon
and Gilmartin (1973) estimated that it takes between 10,000 and 100,000
chunks to reach expertise (50,000 chunks is often cited as a first approxi-
mation). The sheer size of this number led Holding (1985, 1992) to propose
an alternative hypothesis, stating that only 2500 chunks would be enough
if we assume that patterns are encoded abstractly, and independently of
colour and location. For example, the same LTM chunk would encode a
pattern shifted horizontally, vertically, or diagonally by one or several
squares, because the functional relations (e.g., attack, defence) among the
pieces would be maintained.
   To test these alternative hypotheses, Saariluoma (1994) divided positions
into four quadrants, and swapped two of these quadrants diagonally (see
Figure 5.7). If the chunking theory is correct, recall performance should
be higher with nonmodified positions than with modified positions, because
the former should allow the recognition of more chunks than the latter. By
contrast, Holding’s proposal of a generic encoding predicts no difference
between the types of positions. Saariluoma found that the recall of the pieces
in the swapped quadrants was dramatically reduced in comparison with
the recall of unchanged pieces. Converging evidence was provided by Gobet
and Simon (1996a), who modified positions using various mirror-image
reflections (e.g., white and black, or left and right are swapped; see Figure
5.8). They found that distortions around the vertical axis impaired recall
reliably, although the effect was small.
   In summary, these results support the hypothesis that spatial location is
encoded in chunks and add plausibility to Simon and Gilmartin’s estimate
that at least 50,000 chunks are necessary for expertise. Using a simplified
88   Moves in mind




Figure 5.7 Example of the kind of position modification used by Saariluoma (1994),
           which swaps two quadrants of a position: (a) before swapping; (b) after
           swapping.


chunking model, Gobet and Simon (1996a) carried out simulations of the
mirror-image modification experiments, and found that the model obtained
the same effects as those obtained with human players.


Mode of representation
With chess, both the chunking and template theory propose that, while
players use a number of modalities, the main access to chunks is visuo-
spatial, which is the representation used during most of a player’s learning
and training time. In particular, they postulate the presence of an internal
system (‘the mind’s eye’), which uses a visuo-spatial mode of representation
and carries out mental operations on perceptual structures. There is now
overwhelming evidence for such a system from research in psychology and
neuroscience (e.g., Kosslyn & Koenig, 1992).
   Several studies support the importance given to visuo-spatial representa-
tions in chess. Chase and Simon (1973b) directly explored the role played
by the mode of stimulus presentation. They displayed half of the positions
with standard board and pieces, and the other half with diagrams containing
letters. The same dichotomy was used during recall. Stimulus modality,
but not response modality, influenced recall percentage. The effect was
rather large with stimulus modality: their class A player obtained about
twice as many correct pieces with board presentation as with letter diagrams.
Interestingly, this difference disappeared rapidly with practice: after about
                                    Memory, knowledge, and representations          89




Figure 5.8 Example of the types of position used in Gobet and Simon (1996a). The
           same position is presented (a) under its normal appearance; (b) after reflec-
           tion about the horizontal axis; (c) after reflection about the vertical axis:
           and (d) after reflection about the central axes.

one hour of training, their subject did not show any difference in the recall of
boards and letter diagrams.
   In another experiment, class A players did not show any difference in the
recall of positions shown with diagrams (such as the ones found in chess
journals or books) and positions with real pieces and board. By contrast,
the beginner was sensitive to these differences in modality. This result can be
related to a study of Go and gomoku, where Eisenstadt and Kareev (1977,
p. 549) used Xs and Os instead of black and white stones, and played on the
90   Moves in mind
squares instead of the grid intersections. They assumed that these changes
preserved the essential characteristics of both games. They also suggested
that players had a subjective perception of positions that did not always
correspond perfectly with the actual positions. This suggestion is largely in
line with the chess research just discussed.
   Charness (1974) carried out an ingenious study to test the hypothesis
that statements describing a chess position were represented with a spatial
structure. His experiment was inspired by Brooks (1967), who found that it
was better to listen to than to read sentences referring to spatial representa-
tions, presumably because the visuo-spatial processing required by reading
would interfere with processes required for holding the spatial represen-
tations. Similarly, Charness found that chessplayers had a better recall
when they listened to the description of a position than when they
read it. (Charness used a reduced version of the chessboard: 4×4 matrices
that contained eight pieces.) No difference was to be found with non-
players. Moreover, an imagery scale showed that visualization decreased
in the reading condition. In a similar vein, Charness (1974) found that
recall was better when positions were presented visually rather than
aurally.
   Robbins et al. (1995) used a different approach to study the way chess-
players represent positions, and asked players to carry out various interfering
tasks during their presentation. Their research was motivated by Baddeley
and Hitch’s (1974) theory of working memory, which divides working
memory into an articulatory loop (storing verbal material), a visuo-spatial
sketchpad (storing visual and spatial information), and a central executive
(coordinating the information flow between the other two subsystems). They
found that a verbal task (repeating ‘the’) had a negligible effect on recall
performance, while a visuo-spatial task (keying in a sequence of keystrokes),
and a task aimed at suppressing the central executive (generating a random
string of letters, one per second) occasioned a significant loss of performance
(more than 66% in comparison with a control task without interfering
task). Similar effects were found on a problem-solving task, although per-
formance was not impaired as drastically (only about 33%). Some of these
results—effect of visuo-spatial interference and absence of effect of articula-
tory interference—were also found by Saariluoma (1992b) and Saariluoma
and Kalakoski (1998).
   In earlier work, Saariluoma (1991) had combined this concurrent memory-
load paradigm with blindfold play. He dictated sequences of moves from
games whereby moving a single piece took 2 s, and asked players to describe
the location of all pieces after moves 15 and 25. After the dictation of each
individual move, subjects had to carry out the interfering task. Consistent
with the results just reviewed, Saariluoma found that concurrent interfering
tasks had a negative effect on performance when they were visuo-spatial
or related to the central executive, but not when they were articulatory.
Saariluoma also carried out an experiment where interference occurred after
                                  Memory, knowledge, and representations        91
the dictation of a sequence of moves. The three interfering tasks had no effect
in this case.


Representations used in blindfold playing
One final source of evidence for the type of representation used in game
playing comes from masters’ ability to play blindfold. We have already
mentioned this variant of play when discussing memory for move sequence
and the role of input modality. In blindfold games, a player carries out one
or several games without seeing the board, typically against opponents
who have full view of the board; the moves are communicated aloud using
standard notation (e.g., the algebraic notation for chess: 1. e2-e4 e7-e5;
2. Ng1-f3 Nb8-c6, etc.). The literature on blindfold play has concentrated
on blindfold chess and to a lesser extent on blindfold draughts (Keessen &
van der Stoep, 1986). It is known that blindfold trictrac is also possible,
but this is not well documented. There are various accounts of blindfold
shogi (Iida, 1995)—Japanese chess—but blindfold Go does not seem
common.
   The literature on blindfold play consists of interviews with blindfold players
(Binet, 1894; Mieses, 1938), documented games (Iida, 1995; Koltanowski,
1990), anecdotes of blindfold exhibition games (Keessen & van der Stoep,
1986; Steinkohl, 1992), and speculation by the authors. Experimental studies
are rarer.


Informal accounts
In general, the blindfold-play literature assumes that the physical presence of
the board and pieces needs to be somehow recreated internally. This of course
relates to the question of visualization—a term which is not well defined in
the literature. It usually means that something is imagined by forming a
picture in the mind, although the exact nature of this picture (e.g., whether
it is permanent or transient) is left unclear. According to these informal
reports, sometimes this picture contains the actual shape of the board and
pieces, sometimes the abstract contours or essential physical characteristics
are visualized. In all cases the position on the external board needs to be
remembered. Let us consider the detail of these introspective reports first
with chess, and then with other board games.
   Binet (1894, 1966) sent informal questionnaires to the best players of the
time, asking them to describe what they were doing when playing blind-
fold chess. In particular, he was interested in the characteristics of their repre-
sentations—that is, what they ‘saw’. Players’ responses indicated that they
typically did not encode the physical characteristics of the board or the style
of the pieces; some thought that their image contained the fuzzy contours
of the board and pieces; others reported an abstract type of representation.
While somewhat confirming Binet’s belief that visualization was part of
92   Moves in mind
the processes involved in blindfold chess, these comments also led Binet to
conclude that knowledge, and not concrete visual images, was critical.
   Later research supported Binet’s view. Former world champion Alekhine
noted that what matters in (simultaneous) blindfold chess is logical,
rather than visual, memory (Bushke, 1971). In an introspective account,
Fine (1965)—a world class player in his youth, and later a renowned psycho-
analyst—stressed the role of chess knowledge, including that of hierarchical,
spatio-temporal Gestalt formations, which makes it possible for strong
players to grasp the positions as a whole. Fine also noted the possible inter-
ference between similar games, and the use of key statements for sum-
marizing positions. For him, the use of a blank chessboard was more of a
hindrance than a help, although other masters, such as Koltanowski, who
held the world record for the number of simultaneous blindfold games, found
this external aid helpful (Koltanowski, 1990). Contrasting with most
accounts, however, Fine also emphasized the capacity to visualize the board
clearly. Dextreit and Engel (1981), who offer a comprehensive review of the
literature on blindfold chess, suggest that players encode positions using key
sentences (e.g., ‘Panov attack: white builds up an attack on the King’s side,
black tries to counterattack on the centre’), which map onto the critical
moments of the game.
   Keessen and van der Stoep (1986) insist that blindfold draughts is more
complicated than blindfold chess because the pieces are similar. They also
suggest that not all blindfold players visualize. Similarly, shogi players insist
that blind shogi is more complicated because of the re-entry of pieces (Iida,
personal communication). For mancala games, only one instance has been
recorded, which will be discussed below.


Empirical data

Chess
So far, we have restricted our attention to anecdotal and informal evidence.
Indeed, this type of evidence has for a long time dominated the field, and only
with the series of clever chess experiments performed by Pertti Saariluoma
did we finally obtain a systematic and controlled study of blindfold play. As
we have seen earlier in this chapter, Saariluoma (1991) presented one or
several games aurally or visually, with or without the interpolation of inter-
fering tasks. Saariluoma identified several phenomena about blindfold chess:
first, it engages mainly visuo-spatial working memory and does not make
much use of verbal working memory; second, differences in LTM knowledge
(e.g., number of chunks and type of knowledge associated with them),
rather than differences in imagery ability, underlie skill differences; and third,
visuo-spatial working memory plays a key role in early stages of encoding,
but not in later processing.
   In a continuation of this line of enquiry, Saariluoma and Kalakoski (1997)
                                 Memory, knowledge, and representations     93
identified further issues. First, they found that replacing chess pieces with
dots had relatively little effect on masters’ and medium-class players’ memory
performance. This result suggests that the location of the piece being moved,
and not information about its colour or size, offers critical information. This
clearly corroborates Binet’s (1894) conclusion that abstract representations
are essential in blindfold chess. Second, performance was strongly impaired
when the two halves of the board were transposed; Saariluoma and Kalakoski
proposed that this deficit was due to the time needed to translate between the
perceived patterns and the chunks stored in LTM. Third, they found that
there was no difference between auditory and visual presentation. And,
finally, less skilled players increased their performance with additional time,
although they still could not reach the performance of highly skilled chess
players.
   In further experiments, Saariluoma and Kalakoski (1998) investigated
blindfold players’ problem-solving ability with dictated chess positions. In a
recognition task, players memorized functionally relevant pieces better than
functionally irrelevant pieces; this difference vanished when players’ attention
was directed towards superficial features (counting the number of white
and black pieces) rather than semantically important features (searching
for white’s best move). Finally, players performed better when a tactical
combination was possible in a game position compared to a random position.
   Campitelli and Gobet (in press) addressed the question of how perception
filters out relevant from irrelevant information. In two experiments, chess
games were presented visually, move by move, on a board that contained
irrelevant information (static positions, positions of another game changing
every 10 ply, and positions changing every move). Results indicated that
irrelevant information affected chess masters only when it changed during the
presentation of the target game. This suggests that novelty information is
used by human perception to select incoming visual information and separate
‘figure’ and ‘ground’.
   To account for the outcomes of their experiments, Saariluoma (1991) and
Saariluoma and Kalakoski (1997, 1998) borrowed ideas from several theories.
These include Chase and Simon’s (1973a, 1973b) chunking theory, Ericsson
and Kintsch’s (1995) long-term working memory theory, Baddeley and
Hitch’s (1974) working-memory theory, and Leibniz’ (1704) concept of
apperception (i.e., second-order perception). Campitelli and Gobet (in press)
show how most of these results can be explained within a single framework—
that provided by the template theory.
   Although not strictly investigating blindfold chess, two other experiments
studying mental imagery may also be mentioned here. In Milojkovic’s (1982)
study, participants were presented with a chess position containing three
pieces for three seconds; they were then required to perform a capture
mentally; finally, they had to decide if a new position presented on the screen
matched the position obtained after the capture. With novices, Milojkovic
found a linear relation between reaction times and the number of squares
94   Moves in mind
separating the two pieces involved in the capture. The master’s reactions
times were constant. In a second experiment, the position before capture
remained visible on the screen when the move had to be performed. This
provided a perceptual baseline against which to compare the results of the
imagery task. Although the master’s reaction times were globally faster, both
novices’ and the master’s reaction times were a linear function of the distance
separating the two pieces. As few subjects took part in these experiments and
some of the results could not be replicated (Charness, 1991), caution should
be exercised in interpreting these results (see also de Groot & Gobet, 1996).
   Bachman and Oit (1992) used a moving-spot task, where participants had
to imagine an 8×8 grid or a chessboard, and move either a spot or one of the
chess pieces according to a sequence of up, down, right or left instructions.
While no skill differences were found in the moving-spot condition, chess-
players committed fewer errors than nonplayers in the moving chess-piece
condition. In this condition, there was also a tendency for skilled players to
show Stroop-like interference (see Chapter 4) when the piece had to move
illegally (e.g., a Bishop moving up or right). Finally, all players did better
when imagining a chessboard rather than an 8×8 grid.


Other board games
In bao, there are three problems with the concept of visualization as employed
above. First, there is little evidence for perceptual recall of bao positions
as there is of chess positions. Second, it is impossible to visualize certain
positions, since holes containing more than eight counters need to be emptied
before their precise content is clear. Third, the changes in the game cannot
be calculated by visualizing the moves, since a move does not result in
incremental but in multiple changes on the board that need to be calculated
individually.
   Experiments on blindfold bao raise additional difficulties. First, the player
has to play blind and deaf bao, since hearing the ticking of the seeds assists
his calculating efforts—an auditory mnemonic aid. Second, there are moves
that no master can calculate, even with the visual presence of a board, such
as moves that continue for more than seven rounds. Therefore, it is always
possible that a player of blindfold bao loses track of the game. The task of
a master is to prevent such moves, by not playing them and not giving the
opponent the opportunity to play them. According to bao masters, such a
strategy of preventing long ‘duru’ (rounds) is within their capacity and
should not prevent the ability to play blindfold bao.
   One bao master was trained by de Voogt (1995) to play blindfold with the
help of a notational system. After one year, this master was able to play a
blindfold bao game 40 ply long. Two years later a blindfold simultaneous
exhibition game resulted in two games of that length being played in front of
an audience (de Voogt, 1997).
   In all stages of the blindfold game, the master was not able to give the
                                 Memory, knowledge, and representations      95
present position on the board without taking considerable time in calculating
the contents of each hole. Some parts of the board, in particular those
recently played, would be given quickly, but others would take minutes. This
is contrary to what has been observed with blindfold chess and draughts,
where players can give the present position without any hesitation (e.g.,
Ericsson & Oliver, 1984).
   All players of blindfold games remember the moves they have played. In
difficult situations, they sometimes use this information to reconstruct
the position on the board—a phenomenon also found in blindfold chess (cf.
Binet, 1894). De Voogt (1998) suggests that reconstruction is the fundamental
skill used in blindfold bao that largely bypasses position recall skills and
visualization. The player used various stratagems to reduce the volatility of
the position by using a larger part of the board in the opening game. Position
recall would have been complicated by this stratagem and the unfamiliar
opening strategy reduced the advantage of opening experience. The
restriction of volatility appeared crucial in the later stages to allow progress
towards blindfold simultaneous games.


Knowledge and memory schemata
Referring to the distinction proposed by Tulving (1972) between episodic
and semantic memory, Holding (1985) notes that, while one knows almost
nothing about the former with respect to chess, more data have been collected
about the latter. The same conclusion could be made about other board
games.


Contextual information and high-level knowledge
In our discussion of perception and categorization in Chapter 4, we have
already touched on conceptual and contextual knowledge. More evidence has
been collected about this topic within the framework of memory research.
Several experiments have established that supplementary information, even
of an abstract kind, enhances subjects’ memory for positions. Goldin (1978a)
let her subjects study the moves leading to the stimulus position. She
found that study of the previous moves significantly increased both recall
performance and subjects’ confidence. Similar results were obtained by Frey
and Adesman (1976). It should be pointed out that, in these two experiments,
the supplementary-information variable was confounded with the presenta-
tion time variable (Gobet, 1993b). By contrast, partial cues about the
position, such as the location of a few pieces, do not improve recall of the
noncued pieces, with neither tournament players nor occasional players
(Huffman, Matthews, & Gagne, 2001; Watkins, Schwartz, & Lane, 1984).
   As in other domains, such as verbal memory (Craik & Lockhart, 1972),
recall performance depends on the level of semantic processing with which
subjects examine a position. Lane and Robertson (1979) manipulated the
96   Moves in mind
level of processing by using different instructions. In the ‘formal orienting’
condition, players had to count the number of pieces located on white and
black squares; in the ‘meaningful orienting’ condition, players were asked to
evaluate the position and to find the best move. At all skill levels, recall
performance was better in the meaningful processing task than in the formal
task. This difference disappeared when players were warned beforehand
that they would have to reconstruct the position. As we have seen earlier,
better results with a semantic rather than a formal task have also been found
with recognition tasks (Goldin, 1978a).
   Indirect evidence about the presence of high-level representations in
chessplayers comes from the analysis of verbal protocols in problem-solving
tasks (de Groot, 1946), from recall tasks (de Groot, 1946; Gobet, 1993b), and
from classification tasks (Freyhoff et al., 1992). There is direct evidence as
well. Cooke et al. (1993) carried out an experiment where they manipulated
the presence of high-level representations, such as ‘Sicilian-Dragon with
opposite-side castling. White is attacking the kingside, Black the queenside’
(Cooke et al., 1993, p. 326). They found that players took advantage of a
high-level description only when it was given before the presentation of
the position. Finally, the hypothesis of hierarchical representations of chess
positions in memory has also received substantial evidence (Freyhoff et al.,
1992; de Groot & Gobet, 1996; Jongman, 1968).
   Two studies with children may be mentioned here, as they clearly related to
the role of supplementary information in memory. Horgan and Morgan
(1990) have tackled this question with chessplaying children (skill level
between Elo 1100 and 2100). Memory performance reliably correlated with
skill level and age, but this relationship disappeared when children received
contextual information (such as ‘white to play. White is ready for an attack’)
during the presentation of the position. In their study of awele in Ivory
Coast, Retschitzki et al. (1984) compared boys’ memory for awele positions
in two conditions: first, following a brief presentation of a real board; and,
second, following an interruption after playing a few moves in a game (with
forced moves to achieve the same end position). In the former condition,
the good players performed significantly better than the weaker players; but
when the reconstitution of the board followed an interrupted game, both
groups were similar in performance. For Retschitzki et al., this result con-
firmed an interpretation in terms of interaction between short-term and long-
term memory, the weaker players being able to compensate their lack of
knowledge with other clues when they could play some moves of the game.


Verbal knowledge
According to Holding (1989), chessplayers have a large amount of verbal
knowledge, including: (a) rote knowledge of games (one’s own or games
taken from the literature); (b) specific knowledge of opening theory; and (c)
general knowledge of principles for openings, middlegames, and endgames.
                                 Memory, knowledge, and representations      97
Using a multiple-choice questionnaire, Pfau and Murphy (1988) showed
that the amount of specific verbal knowledge was a reliable predictor of chess
skill. An Expert (Elo 2000–2200) had about 55% more knowledge than a class
C player (Elo 1500). In Pfau and Murphy’s sample, chess knowledge was
a better predictor of chess skill than memory for positions (the respective
correlations were 0.69 and 0.44). Gobet (1993b) notes that the generaliz-
ability of these conclusions may be limited to the range of skill levels studied
by Pfau and Murphy (their sample had only three masters above Elo 2200),
and, in particular, may not be applicable to higher levels of expertise. In this
respect, the reader should be reminded of several experimental results that
emphasize visual encoding, and thus contrast with an emphasis on declara-
tive knowledge and verbal encoding. These data indicated the supremacy of
visual encoding (Charness, 1974) and the small effect of articulatory inter-
fering tasks (but not of visuo-spatial tasks) in various chess tasks (Robbins
et al., 1995; Saariluoma, 1992b).


Knowledge and information processing
In an intriguing experiment, Britton and Tesser (1982) demonstrated that
chess knowledge was activated during the choice of a move. Players had to
find the best move in a given position, while simultaneously responding
to auditory stimuli. All players were slower during the initial stage of the
move choice, when most knowledge processing presumably took place.
Moreover, tournament players (class A players) were in general slower than
novices. This result, consistent with two other similar experiments carried
out by Britton and Tesser (1982), seems to indicate that the engagement of
prior knowledge uses part of the information-processing capacity, leading
to deficits in attention—a rather unexpected limit in expertise. As noted
by Gobet (1993b), these results may be limited to an intermediate level of
expertise and may not generalize to master or grandmaster levels.


Typicality
Presumably, the use of high-level representations correlates with position
typicality, a topic that has been studied by several researchers. As seen
earlier, Goldin (1978b) found that typical positions were better recalled and
recognized than atypical positions by subjects of all skill levels. To explain
these results, Holding (1985) suggested that highly typical positions may lead
to the creation of prototypes, which act as schemata to which corrections may
be added. Similar ideas were proposed by Hartston and Wason (1983),
Jongman (1968), and Lories (1984).
   Studying typicality requires some measure of similarity; Horgan, Millis
and Neimeyer (1989) developed a repertory grid technique to examine
how expertise affects similarity judgements. With this technique, players first
generated personal dimensions to characterize chess positions, and then used
98   Moves in mind
these dimensions to rate the same positions. Horgan et al. found a curvilinear
relationship, with Experts generating more independent dimensions than
both novices and masters. They suggest that, as it develops, expertise goes
first through a phase of increasing differentiation, and then a phase of
integration.
   Due to their volatility, the distinction between meaningful and random,
or even typical and atypical positions, does not appear useful with mancala
games. Retschitzki et al. (1984) asked 38 subjects (boys aged 9 to 15)
to reconstruct several awele positions differing according to the number of
occupied holes (4 to 7), the mode of representation (photos, digits, dots),
and the meaning of the position (no threat, single threat, double threat,
reciprocal threat). The best players performed better, but there was no signifi-
cant difference according to the kind of position. According to Retschitzki
et al., the subjects discovered that attending to the characteristics of the
position is not the best memory strategy. Instead, they chose less specific but
more appropriate short-term memory techniques.


Retrieval structures
In recent years, the concept of a ‘retrieval structure’ has played an increasingly
important role as an explanation for expert memory (Chase & Ericsson, 1982;
Ericsson & Kintsch, 1995; Richman, Staszewski, & Simon, 1995; Saariluoma
& Laine, 2001). Retrieval structures denote retrieval cues organized in
stable structures. (The exact meaning of the term has been subject to some
discussion; see Ericsson & Kintsch, 2000; Gobet, 2000a, 2000b, 2000c).
Ericsson and Oliver (1984; see also Ericsson & Staszewski, 1989) were inter-
ested in finding evidence for this concept. In an experiment about the speed
with which chessplayers can access information in their ‘mental chessboard’,
they asked an Expert to memorize a 40-move game blindfold. During the
test phase, the entire board was probed in a random way, and the player was
asked to name the piece (if any) located on a given square as fast as possible.
Although he memorized the game rapidly, taking only 2 s to make a move, he
was accurate and fast (around 2 s) in answering the probes (over 95% correct).
   In another experiment, their subject had to memorize two positions. He
was then probed with three presentation orders: (a) one position was probed
before the other (sequential condition); (b) each position was alternatively
probed (alternating condition); (c) squares were randomly selected from
either position. After a few trials, a stable pattern was apparent: the random
and alternate conditions showed similar reaction times (2.4 s and 1.9 s per
probe, on average), while the sequential condition’s probe became almost
twice as fast (about 1 s). In the sequential condition, there was a peak when
the first square of the new board was probed (about 1.4 s), after which it took
only about 1 s per square for the remainder of the position.
   Ericsson and Staszewski proposed that their subject was using the same
retrieval structure for the two positions, because he could access only one
                                 Memory, knowledge, and representations     99
position at a time—as witnessed by the increase in reaction time when
switching positions and the speed-up when the position stayed the same.
There are, however, other explanations for these results. For example, the
increased latency could be due to the switch between two different retrieval
structures or two templates (Gobet, 1998b).


Board games and mnemonics
One plausible extension of the previous experiment is to investigate how
board games may be used as a mnemonic aid. A number of experimenters,
including Luria (1968), and Hunt and Love (1972) have shown that
mnemonists can successfully memorize briefly presented matrices of random
numbers. Due to the fact that matrices can be used to represent boards
in several games, it therefore seems natural to explore whether board-game
players can use the board as a ‘retrieval structure’. De Voogt (1995) found
that bao experts showed no interest and expertise in memorizing number
matrices. By contrast, Schoen (1996) showed that students familiar with
Monopoly can use the board to help memorize lists of objects. It should
be pointed out that these students, enrolled in an introductory psychology
course, also received basic instruction about memory and about how to
improve it using mnemonics. This instruction was absent in the bao
experiment.


Discussion

Chunking and template theories
One of Chase and Simon’s motivations in developing the chunking theory
was to explain chessplayers’ memory for briefly presented positions. Thus, it
is not surprising that the theory did well in accounting for the recall of game
positions. The two limitations of its computer implementation, MAPP—
chunks were selected by the programmers, and the program did not reach
master level—have been removed in the CHREST implementation of the
template theory. CHREST accounts not only for the percentage correct, but
also for variables such as the number and type of errors, the number and size
of chunks replaced, as well as the pattern of relations within chunks (Gobet,
2001b; Gobet & Simon, 2000a).
   MAPP and CHREST also do well with the recall of random positions.
They correctly predict that, the closer the position is to a game position,
the stronger the skill difference in recall should be, because more and
larger chunks can be accessed. In addition, the skill differences with random
positions are explained by the presence in these positions of a few occasional
patterns, which are more likely to be recognized by large networks. Both
programs replicate how the graded randomization affects recall, from mild
modification by mirror-image transformation (Gobet & Simon, 1996a),
100   Moves in mind
through the standard random positions (Gobet & Simon, 1996b, 2000a),
to the ‘truly random’ positions (Gobet & Waters, in press). CHREST also
simulates in detail how the duration of presentation time affects performance
of players at various skill levels (Gobet & Simon, 2000a). According to the
model, additional time allows players both to recognize additional chunks
and to acquire new chunks. This experiment was a strong test for several
components of the theory, including the use of templates and the time
parameters used with learning.
   Data about board games other than chess are more scarce, but in general
are consistent with the chess data, and thus with chunking mechanisms. The
exception was bao, where no skill effect was found. Only one bao master was
tested in the memory-recall experiment, so we must remain cautious in our
conclusions. In any case, the high volatility of bao positions could explain
why perceptual chunking is harder in this case (see also the results with
Othello). Chunking mechanisms essentially pick up regularities in the
environment; if the environment is unstable, the mechanisms will acquire
perceptual chunks slowly. In this case, chunking mechanisms will pick up
other types of regularities, if any, such as the regularities present in the
sequence of moves, as suggested by de Voogt (1995).
   Following Simon and Gilmartin’s (1973) predictions about the number
of chunks in LTM, several studies have tackled the question of whether
chunks encode the specific location of pieces, or just their relations. The
data from recall experiments support the original hypothesis of Simon and
Gilmartin (information about location is encoded), which follows naturally
from the mechanisms embodied in MAPP and CHREST (Gobet & Simon,
1996a). The data from recognition experiments suggest the use of cues such
as geometric patterns as well as relations of defence and attack.
   As seen in Chapter 3, the chunking theory proposes that, during the
presentation of a board, pieces are encoded in a limited-capacity STM. It
also assumes that LTM encoding is slow (8 s to create a new chunk, and 2 s to
add information to an extant chunk). Thus, the theory predicts that not much
information can be stored if the presentation is short and STM information
is wiped out with an interfering task. This has been tested by several studies
using interfering tasks or multiple positions. Overall, these studies have
shown that interfering tasks do not affect chess memory much, indicating
weaknesses in the chunking theory.
   As retention in STM is reduced in the aforementioned tasks, these results
imply that players can code the positions into large chunks (see also Chapter
4), which then occupy only one slot in STM, and/or that some information
can be transferred rapidly to LTM. Gobet and Simon’s template theory
combines these two explanations. It proposes that common chunks become
schema-like structures with slots, and that information can be encoded
rapidly into these slots, in about 250 ms. The advantage of this explanation is
that it gives a clue as to why the multiple board task is possible for masters
with few boards, but becomes intractable with more than four or five boards:
                                Memory, knowledge, and representations     101
with few boards, only one template per position needs to be stored in STM.
With additional boards, further information must be encoded in LTM
(e.g., encoding of episodic cues), but such information may be subject to
interference from other items in LTM.
   The data on recognition experiments seem consistent with the chunking
and template theories, although no detailed simulation has yet been carried
out. The same applies for memory for moves. In this case, a possibility is
to use the CHUMP model (Gobet & Jansen, 1994), which has mechanisms
for acquiring sequences of moves and associating them with perceptual
chunks. Particularly relevant in this context is Saariluoma’s (1991) blindfold
experiment where legal, random legal, and random illegal moves were
dictated. As we have seen, masters were almost perfect in recalling the
position for the actual games and legal random games after 15 moves, but
had huge difficulties with the random illegal games. Saariluoma explained
these results using the chunking theory, noting that chunks are easier to find
in game positions than in random legal positions, and easier in random legal
positions than in illegal random positions, because the latter diverge from
game-like positions faster than the former. The template theory proposes two
additional mechanisms. First, players can chunk sequences of moves, which
favour strong players (they have stored more and longer sequences of moves).
Second, templates also make storage easier, which again favours stronger
players. As one moves away from game-like positions, it becomes harder to
use these two mechanisms. In general, Campitelli and Gobet (in press) argue
that most of the available data on blindfold chess can be accounted for by the
template theory.
   As proposed by both the chunking and template theories, chessplayers
primarily use a visuo-spatial mode of representation (Charness, 1974). This
visuo-spatial mode seems to be used even in encoding the type of verbal,
serial inputs used by Saariluoma (1989, 1991). One possibility is that infor-
mation about the location of single pieces is stored in the mind’s eye briefly,
which allows chunks to be recognized. Note also that the relatively long time
used for dictating pieces in Saariluoma’s experiments makes it possible
for players to create new chunks. The template theory explicitly proposes
that several routes (visual, verbal, or conceptual) can lead to the same LTM
chunk. Once this chunk is retrieved, it is possible to access the visuo-spatial
representation encoded for it.
   While the chunking theory emphasizes the role of perceptual aspects in
chess expertise, this does not mean that it denies the importance of concep-
tual knowledge (cf. Chase & Simon, 1973b). The same applies to the template
theory, which actually offers computational mechanisms for learning and
using conceptual knowledge, as templates can be seen as conceptual proto-
types. Indeed, while the experiments on conceptual knowledge have often
been taken as evidence against the chunking theory (Cooke et al., 1993;
Holding, 1985), some of these data directly support the template theory, and
sometimes even the chunking theory.
102   Moves in mind
   Consider the experiments where the levels of processing are varied. It has
been argued that these data count against the chunking theory (Holding,
1985) because attention is assumed to be rigid. However, as we have seen in
Chapter 3, the chunking theory is closely related to Feigenbaum and Simon’s
(1962, 1984) EPAM theory, in which attention plays an important role. In
particular, attention determines what kind of chunks will be placed in STM
and learned in LTM. Manipulating the instructions given to subjects, as was
done in chess by Lane and Robertson (1979) and in a concept formation task
by Medin and Smith (1981; see also Gobet, Richman, Staszewski, & Simon,
1997), will direct attention to different aspects of the stimuli, and thus lead to
a different recall performance.
   High-level representations are not tackled explicitly in the chunking theory,
which focuses on how low-level representations (chunks) get constructed.
By comparison, the template theory proposes mechanisms on how chunks
evolve into more complex and higher level data structures (templates). It is a
direct consequence of the template theory that high-level descriptions of
positions are more useful before their presentation than after (cf. Cooke et al.,
1993). In the former case, the high-level description allows subjects to rapidly
access a template, which can be used during the presentation of the position
to fill in information into the template slots. When the description is pre-
sented after the position itself, the template is less useful, as it is accessed later
and only the information left in STM after the presentation of the position
can be used to fill in slots.
   While MAPP simulated only the visual intake of chess positions, there is
nothing in the chunking theory that precludes other routes to chunks—for
example, using verbal labels referring to high-level representations. Indeed,
the EPAM framework, from which the chunking theory derives, has been
used to simulate verbal learning behaviour (Feigenbaum & Simon, 1984), and
the acquisition of syntax and vocabulary by children (Freudenthal, Pine, &
Gobet, 2001; Gobet et al., 2001; Gobet & Pine, 1997; Jones, Gobet, & Pine,
2000). The template theory is explicit about this issue by emphasizing that
several discrimination routes may lead to the same chunk.
   One final topic of research is that of retrieval structures, which has recently
generated a great deal of interest. Chunking mechanisms have been used to
simulate this idea in the digit-span task (Richman et al., 1995) and in chess
(Gobet & Simon, 2000a). Here, the standpoint of the template theory is that
one can distinguish between at least two types of retrieval structures; first,
structures under conscious control that have been learnt deliberately; and,
second, structures (templates) that are learnt implicitly during the intensive
interaction with the domain of expertise. The training experiment described
by Gobet and Simon (1996c) illustrates the difference between these two
types of memory structure.
   In summary, as shown by Gobet (1998a), both the chunking and template
theories account for a fair amount of data on memory, knowledge, and repre-
sentations. The template theory does better in domains such as interference
                                Memory, knowledge, and representations      103
experiments and high-level knowledge, but this is mainly due to the fact
that mechanisms were added with hindsight to the chunking theory to show
how LTM storage can occur rapidly and schemata be created based on
chunks. Science is in the detail, and a clear superiority of these two theories
over alternative accounts is that at least part of their mechanisms has been
embodied in computer programs. In particular, computer simulations
with CHREST have accounted for a number of the phenomena we have
reviewed, including the differential recall of game, random and truly random
positions, the effect of mirror-image modifications on recall, and the role of
presentation time on recall.


Knowledge-based accounts
As seen in Chapter 3, several theories have emphasized the qualitative
organization of expert knowledge. One could add to these theories Binet
(1894), Cleveland (1907), and Holding (1985), who all paid due attention to
high-level knowledge. Researchers having worked in Craik and Lockhart’s
(1972) framework of levels of processing could also be classified under this
label. There is no doubt that the concepts used by these authors—schemata,
high-level knowledge, deep knowledge, and so on—capture important
aspects of board-game expertise. Nevertheless, the lack of detail of these
proposals makes it difficult to test them against empirical data. These
accounts are also rather weak in explaining the skill effect found in recall of
random positions, where high-level knowledge structures are by definition
unavailable.


Long-term working-memory theory
Ericsson and Kintsch (1995, 2000) have argued that the long-term working-
memory theory accounts for most data on chess memory and blindfold
chessplaying, a claim that has been contradicted by Gobet (1998b, 2000c).
One of Gobet’s arguments is that the theory is not specified enough to allow
detailed predictions. For example, the nature of the retrieval structure is not
sufficiently spelled out for this purpose. As is clear in the exchanges spawned
by this controversy, there is a clear disagreement between the two sides over
which is the better form of psychological theory: detailed computational
models on one side, or more abstract mechanisms on the other. We hope
to have convinced the reader that developing computational models
considerably increases the prospects of understanding board-game cognition.


The constraint-attunement hypothesis
The constraint-attunement hypothesis (Vicente, 2000; Vicente & Wang, 1998)
is another attempt to account for several of the memory recall experiments
we have reviewed in this chapter. The gist of their approach is that experts can
104   Moves in mind
exploit goal-relevant constraints and that the expertise advantage will be a
function of the number of constraints available. The detail of Vicente and
Wang’s analyses has been disputed by Ericsson et al. (2000), and Simon
and Gobet (2000), who also discuss some epistemological weaknesses of
the constraint-attunement hypothesis. The board-game research we have
reviewed in this chapter points to additional weaknesses. Contrary to Vicente
and Wang’s (1998) prediction, there is a skill effect in the recall of truly
random positions. Moreover, the presence of supplementary knowledge,
which increases the number of constraints and should thus increase the
skill effect, has in two experiments led to a disappearance of the skill
effect apparent with board presentation only (Horgan & Morgan, 1990;
Retschitzki, et al., 1984). Finally, this theory eschews the discussion of
internal mechanisms, and is thus silent about topics such as the numbers
and types of error, the number and size of chunks recalled, the mode of
representation used, the role of presentation time, and blindfold chess, to
mention a few.


Conclusion
This chapter contains a rich variety of data, and its length reflects the vigour
with which memory has been researched in board games. We have seen that
the chunking mechanisms included in the chunking and template theories
account for a substantial portion of the data. Even so, an important question
is whether these mechanisms can also explain (aspects of) problem solving
and decision making—the essence of board games. This is the topic of the
following chapter.
6      Problem solving and
       decision making




Research into problem solving and decision making in board games has
focused on the following topics: search, knowledge, planning, and evaluation.
In addition, several researchers have attempted to understand how results
from research into perception and memory can be integrated with results
from research into decision making; a recurring theme is how players manage
to compensate for the strong constraints imposed by memory and processing
limits on the number of states searched. This theme, and the concepts related
to it—selective search, satisficing, progressive deepening—play an essential
role in research on decision making, not only in board games, but in general
(e.g., de Groot, 1946; Simon, 1955).
   This chapter is organized as follows. We first review empirical data on
search behaviour; we then discuss empirical data on the role of perception,
knowledge, and analogy in problem solving; next, we consider various
theoretical models specifically developed to account for problem solving in
board-game playing. Finally, we evaluate the impact of problem-solving
research on general theories of board-game expertise.


Empirical data on search behaviour

Macrostructure of search in chess
In his seminal research, de Groot (1946) provided empirical data charac-
terizing the way chessplayers decide their next move. In particular, he
identified the role of selective search, perception, and knowledge in problem
solving. As was shown by subsequent research, the features identified by
de Groot are also valid in other decision-making and problem-solving
situations (Newell & Simon, 1972). De Groot used a methodology that has
left its mark in chess research (its impact on other board games is less
apparent; see Chapter 10). He asked his participants to think aloud when
trying to find the best move given a position. The verbal protocols were
then analysed to extract various quantitative and qualitative measures of
players’ thinking behaviour. (An example of this type of analysis is given in
Appendix 3.)
106   Moves in mind
   The quantitative analyses, to which de Groot devoted only a handful of
pages, have had much more impact on cognitive psychology than his detailed
qualitative analyses, which run over several hundred pages. We begin by
presenting the quantitative analyses, adding some recent results on chess and
other board games, and then discuss the qualitative results.
   De Groot (1946) could find almost no differences in the macrostructure of
search between world-class grandmasters and Experts—i.e., relatively strong
players. In particular, in spite of the number of years his grandmasters had
spent studying chess, there was little evidence for skill differences in the size
of their search trees. On average, players from both skill levels searched
equally deeply, visited the same number of positions in their search, and
proposed the same number of candidate moves. The only differences
were that his best players proposed better moves, that they were faster at
generating moves, and that they took somewhat less time to reach a decision.
Also, as we shall see below, the branches of the tree they examined were often
more relevant than those examined by weaker players.
   In most of his analyses, de Groot (1946) compared grandmasters with
Experts. As noted by Holding (1985), this may have obscured some of the
effects. Recent research shows some skill differences when weaker players
are included (e.g., Charness, 1981a; Gobet, 1998a; Horgan et al., 1989;
Saariluoma, 1992a). Note also that international masters and grandmasters
sometimes search less than masters, presumably because they rapidly zoom
in onto the correct solution thanks to pattern recognition (Saariluoma,
1990). Based on such results, Charness (1981b) suggested that depth of
search increases up to Expert level, after which it stays uniform. Using com-
puter simulations, Gobet (1997a) reached a slightly different conclusion: he
argued that average depth of search follows a power law of skill—that is, it
keeps increasing with high levels of skills, but with diminishing returns. This
is consistent with the following data: on average, de Groot’s (world-class)
grandmasters searched 5.3 ply deep, and his Experts, whose strength were
about three standard deviations below, searched 4.8 ply deep. Charness’
(1981b) class D players (six standard deviations below world class players)
searched 2.3 ply. It should also be pointed out that the statistics of search
(including depth of search) are affected by the presence of context, such
as partial or full knowledge of the moves that led to the problem position
(Lories, 1987b).


Macrostructure of search in other games
The structure of search depends on the branching factor and the size of
the search tree. While Go generates trees much larger than any other game
presented in this book, awele and bao have limited trees compared to chess.
In awele, there is a maximum choice of six moves and, in bao, the average
number is not any higher. In his study of awele, Retschitzki (1989) asked a few
good adult players to think aloud while considering middlegame positions.
                                   Problem solving and decision making     107
Players had to indicate the best and worst move in each situation, and justify
their choice. The reasons given by these players indicated that they were able
to anticipate at least six ply; another striking result was that they were
thinking in terms of both short- and long-term consequences.
   De Voogt (1995) states that volatility in bao forces experts to consider all
moves in the position at hand, and not to make a first selection before having
done so, unless it is a known situation. The calculation abilities of experts
make their search tree significantly larger and deeper than those of novices.
From interviews, it was deduced that the maximum search depth in bao
history for an average position was 12 ply, and that an average search depth
for an expert would be three moves (6 ply).
   The calculation of a single mancala move can be complex and thereby
require a problem-solving strategy. Novices are sometimes not able to cal-
culate 1 ply, a situation that only occurs in mancala games. De Voogt (1995)
devised experiments in which bao experts were required to calculate a move.
In bao, a sowing uses two rows of eight holes and in these experiments,
between 40 and 50 counters were involved in the sowing. The contents of a
hole are spread one by one to consecutive holes and when the last counter
reaches an occupied hole (also known as a station), this hole is then emptied
in its turn and sown further in the same direction. This relay of sowings, a
characteristic of bao, dakon and other mancala games (with the exception of
awele), is sometimes never ending and requires calculating skills. De Voogt’s
results showed that experts appeared able to calculate such sowings for up
to four rounds independent of the number of stations. When the two rows of
eight holes were reduced to two rows of four holes, the experts were still able
to calculate the same number of rounds.
   It seems that a problem-solving technique used by players consisted in
repeating calculations. To test this hypothesis, the holes were covered with
little cartons and only uncovered by the players when a station was reached
during calculation, eliminating the possibility of repetition. This manipula-
tion reduced the performance to about eight stations when players were
sowing into two rows of eight. It appeared to have the same limitation of
eight stations when players were sowing into two rows of four holes.
   Repetition also allowed the player to focus on the contents of one particu-
lar station. The player repeated the sequence of calculations a number of
times to confirm his calculations. This way, experts were able to calculate
18 stations. De Voogt (1995) links his results to the chunking theory by
describing the chunking procedure for each station in the calculation.
   There are many solutions to the problem of finding the winning opening
move in dakon, which has a search tree comparable to that of checkers. In
dakon, each sowing is only in one direction. In the Maldives, a board of two
rows of eight holes and 128 counters are used. At each end of the board,
there is an enlarged end hole. Each player owns one of those holes. Only a
player’s own end hole is sown into during a move. If a sowing ends in this end
hole the player has the right to choose another hole and start a new ‘move’.
108   Moves in mind
The object of the game is to put as many counters in this end hole as possible.
Clearly, the beginning player has an advantage, and this advantage can be
decisive: in the Maldives, a sequence was found that put more than 120
counters in the end hole before the opponent could make a move. A regular
pattern for playing the sequence could only be found in the first 10 moves;
the remaining moves do not seem to follow any regularity. The solution that
was found by hand consisted of a sequence of 93 moves while computer
analysis showed the shortest sequence to be only 29 moves.
   Donkers, de Voogt, and Uiterwijk (2000) showed that problem-solving
strategies in dakon are also characterized by selective search. Using computer
simulations, they put constraints on the moves in the search tree that a
human player is likely to calculate. Moves with a low number of rounds
were preferred, and moves that took more than four rounds to complete were
eliminated. The constraints explained why this and not another winning
sequence was found. Trial and error in combination with limitations on
calculations predicted a successful search within a reasonable time span.
   This type of selective search holds true for bao as well. Incalculable
moves will limit the number of search nodes and forced moves will reduce
the number of calculated nodes as well. Even though a complete evaluation
of all nodes is attempted, the limited mental capabilities will prevent not only
the number of moves considered but also their complexity.
   Laughlin, Lange, and Adamopoulos (1982) concentrated on concept identi-
fication, using a simplified version of Mastermind. Analysis of the game tree,
as well as previous research on concept identification, suggested two selection
strategies. The ‘focusing strategy’, where the relevance of dimensions is tested
as a whole, is less efficient but requires less insight in the logical structure
of the problem. The ‘tactical strategy’, where moves try to refute half of the
hypotheses, is theoretically more efficient but ‘makes strong demands on
inference and requires relatively deep insight into the anticipated feedback
distributions for potential selections’ (Laughlin et al., 1982, p. 478). Players
who used these strategies were more successful than those who did not. This
was the case both for players who freely chose either strategy, and those
who were induced to do so. (About Mastermind strategies, see also Best,
1990, 2000.)


Qualitative aspects of search in chess

Selective search and move generation
One important finding of de Groot’s study was that all players were selective
in their search. Indeed, they rarely visited more than 100 nodes before
making their decision. According to de Groot, this high level of selectivity,
which is in part due to limits in memory and processing capacity, is also
a hallmark of human cognition in general. De Groot also found that strong
players often zoomed in rapidly onto good moves. Supporting this view,
                                   Problem solving and decision making    109
Klein and Peio (1989) found that Experts were better than novices at pre-
dicting the moves of an unknown game. Experts also needed less guesses
to find the actual move, often finding it in their first attempt. Even under
time pressure, masters can make relatively good decisions. Calderwood,
Klein, and Crandall (1988) found that the quality of masters’ moves
deteriorated little in speed chess (about 5 s per move) as compared with
normal chess (about 120 s per move). A limitation of this study is that move
quality, evaluated subjectively by two grandmasters, may have been an
insensitive measure, as it did not differentiate between masters and class B
players in normal chess. Gobet and Simon (1996d) found that former world
champion Kasparov performed at a relatively high level even when playing
simultaneous games against strong masters and grandmasters. In nine
matches against national teams and against Hamburg, one of the top
teams of Germany, Kasparov reached a median performance that still would
place him in about the six best players in the world. (One of the authors,
FG, had the redoubtable honour to defend the Swiss flag against Kasparov.
An insider’s report of this match, which Kasparov won 5.5–0.5, is given in
Gobet, 1987. We will take up Kasparov’s performances toward the end of this
chapter.)


Phases of move choice
De Groot (1946) proposed that decision-making processes in chess could be
divided into three phases: first phase, progressive deepening, and final phase.
During the first phase, players familiarize themselves with the position,
make a rough evaluation of it (without search), and note the possible
plans, strategic ideas, threats, and potential moves. The boundaries of this
phase and the next are not sharply drawn, as there is some overlap between
enumerating potential base moves (moves playable in the stimulus position)
and carrying out search, which belongs to the progressive-deepening phase.
In the final phase, players recapitulate the outcome of their search, and check
the validity of their decision. The presence of the first phase, including
search-like evaluation of the position, has also been identified in Go
(Yoshikawa et al., 1999).
  Based on the analysis of verbal protocols and eye movements (see below),
Tikhomirov and Poznyanskaya (1966) proposed three stages to characterize
choice behaviour in chess. These stages overlap considerably with de Groot’s
phases (1946). In the first stage, there is a preliminary investigation of
the position, where attention is particularly directed on the opponent’s
moves; some of these moves are selected for further investigation. In the
second stage, base moves are analysed, and their number is progressively
reduced to two; selected variations are then examined more deeply. In
the third stage, a move is selected; this is usually one of the main moves
previously considered.
  Tikhomirov and Poznyanskaya (1966) provide some quantitative
110   Moves in mind
information about these phases. They found that the ratio of one’s own
moves to the opponent’s moves was 1:6 during the first 35 s, 7:4 during
the next 70 s, and 6:3 for the last 30 s. Note that these statistics may be
idiosyncratic to the position used in their experiment. Similarly, Tikhomirov
and Terekhov (1967), who traced the hand movements of a blind chessplayer
(as opposed to a blindfold chessplayer), found that the player limited his
attention to a restricted number of squares. They suggested that the most
important activity during the choice of a move relates to the verification of
hypotheses.


Progressive deepening
De Groot (1946) discovered that players tend to consider the same branches
of the search tree several times, either directly or after visiting other branches.
With each pass, the branch is analysed more fully, either by considering
deeper moves, or by refining the evaluation of the leaf position. De Groot,
who called this phenomenon ‘progressive deepening’, saw two reasons for
this search behaviour: it compensates for limits in human memory and it
propagates information discovered in one branch of the search tree to
other branches (de Groot, 1946; de Groot & Gobet, 1996). This behaviour
can be found in many other tasks, such as scientific research. In this case,
the scientist goes back and forth between different hypotheses and ideas,
producing a spiralling development (de Groot, 1969). Indeed, given that
any good problem solver must use sensitive feedback mechanisms and
incorporate the resulting information back to the search, including revising
old plans, it may well be the case that the reinvestigations characterizing
progressive deepening are inevitable (de Groot, 1946).
   There is some evidence that skill differences exist in the way progressive
deepening is carried out (Gobet, 1998a). Reinvestigations can be divided into
two types: Immediate reinvestigations, where the same base move is analysed
in the next episode, and nonimmediate reinvestigations, where at least one
different move is taken up between the analysis of a base move and its
reinvestigation. Gobet found that the maximum number of immediate
reinvestigations was proportional to the strength of the players, while
the maximum number of nonimmediate reinvestigations was inversely
proportional. We shall discuss additional differences when dealing with the
‘homing heuristic’.


Directionality of search
In domains such as physics and algebra, experts carry out forward search on
simpler problems (e.g., Larkin et al., 1980). That is, they start from the givens
of the problem, and move to a goal state. Instead, novices carry out backward
search: they start from the goal, and move back to the current situation.
Interestingly, on more complex problems, both experts and novices tend
                                    Problem solving and decision making     111
to search backward from the goal. Another pattern emerges in chess, and
probably in other board games, where the direction of search is essentially
forward (Newell & Simon, 1972). This is despite the fact that goals and plans
are used to inform the selection of candidate moves. One reason for this
behaviour is that in most cases, there is no concrete goal at hand, often not
even a single goal, but rather a combination of goals and intentions. Back-
ward search may sometimes occur, for example with positions having a
clear strategic or tactical objective (e.g., in chess, a typical mate pattern or
a promotion opportunity).


Planning
Chess masters often identify adequate plans rapidly and can evaluate
positions swiftly. As de Groot (1946) puts it, masters literally ‘see’ the next
move and the appropriate plan, even before carrying out any search or
applying an evaluation function explicitly. De Groot (1946) provides some
description of planning behaviour, including the development of plans
and the struggle between two competing plans. Saariluoma (1984) covers
planning in his discussion of the role of knowledge in the construction of
problem spaces. In line with de Groot’s results, he documented how
schematic problem spaces are constructed early on in a problem-solving task.
He also presented data about how two elementary problem spaces can be
combined to construct a more complex problem space. Finally, he conducted
experiments on how plans and problem spaces can be abruptly reorganized
following an insight episode.
   When thinking about a position, chessplayers often produce sequences
that have null moves—gaps between some of the moves. This is particularly
apparent with positions that have a strong strategic content. Using the
concept of apperception (see Chapter 3), Saariluoma and Hohlfeld (1994)
explored the role of these null moves in planning. As noted by these authors,
such gaps in plans are quite typical of problem solving outside the realm of
board games (e.g., Selz, 1922). In an experiment where strategic positions
were used as stimuli, it was found that null moves were quite common (about
12% of all moves). This is comparable to the 10% found in a previous study
by Charness (1981b). In a second experiment, Saariluoma and Hohlfeld
(1994) manipulated positions by transposing one relevant piece, so that a
combination present before the transformation was no longer possible.
Essentially, tactical positions were transformed into strategic positions. The
results indicated that the elimination of the combination led to an increase in
the number of null moves.
   Given the importance of planning in the chess literature and the rather
large body of informal evidence that chessplayers use plans (Kmoch,
1980; Kotov, 1971), it is somewhat surprising that there are not more formal
studies on this topic. Clearly, it is a domain in which further research is
necessary.
112   Moves in mind
Evaluating positions
Anecdotal evidence suggests that there are differences in chessplayers’ ability
to evaluate positions (e.g., Krogius, 1976), with players such as Capablanca
or Karpov being known for their speedy and accurate evaluations. Indeed,
Cleveland (1907), basing his conclusions on questionnaire analysis, deemed
‘position sense’ to be the crucial feature of chess skill.
   From de Groot’s (1946) protocols, it appears that evaluations, or at least
their verbal expression, concentrate on one feature at a time, such as ‘white
has more space’, and ‘the square d5 is weak’. Thus, human evaluations are
not comparable to computer evaluations, which combine, usually with a
polynomial function, a large number of features, including control of the
centre, safety of the King, and material balance. Theories such as the
chunking and the template theories suggest that players unconsciously use
more features than those expressed verbally, although no research has
attempted to study the extent of this difference.
   There are two (related) types of evaluation in game playing. The first
applies to the situation currently present on the board; the second applies to
the anticipated positions. Holding (1979) carried out several experiments
investigating the way players evaluate the end positions (the ‘leaves’) of their
search tree. As noted by Holding (1985), empirical work on evaluation is
hampered by the fact that the real value of a given position is usually not
known. For practical purposes, the judgements of masters and the evaluation
provided by computers can be used as a first approximation. Holding con-
sistently found that strong players evaluated positions better than weaker
players (Holding, 1979). This general finding is supported by Charness
(1981a), who asked players to evaluate endgame positions taken from Fine
(1941). When considering the responses given rapidly (under 10 s), Charness
found that the proportion of correct evaluations correlated with chess ratings.
Interestingly, age did not influence the quality of the evaluations.
   Holding (1979) identified several features of evaluation behaviour. As they
become stronger, chessplayers show more discrimination in their judgement,
in particular with endgames; that is, they are more likely to give high (low)
values to positions that are advantageous (disadvantageous) than weaker
players do, who tend to give values closer to equality. Evaluation judgements
are also influenced by potential game continuations, in addition to static
factors. Indeed, as Holding (1985, p. 215) puts it: ‘In computer terms, then,
the human move-evaluation process seems to be iterative or, perhaps,
recursive. Positional evaluations must eventually guide the move choice,
but the nature of the moves considered partly determines the evaluations.’
As noted by Holding, this process may be the basis for de Groot’s (1946)
progressive-deepening behaviour. Finally, players tend to underestimate
their chances and overestimate their opponents’, a phenomenon that may
be related to the rather pessimistic temperament of chessplayers (de Groot,
1946).
                                   Problem solving and decision making     113
   Holding (1979) also found that players’ evaluations correlate with evalu-
ations based on mobility or square control, and with the more sophisticated
position evaluation function used in the Chess 4.5 program (Slate & Atkin,
1977). This program uses a variety of heuristics such as King safety, Pawn
structure, mobility of pieces, etc. Holding (1985) takes this as evidence that
human players behave the same way as computers, but this conclusion may be
premature. First, his human data were obtained with rather weak players
(below Expert level), and it is unknown whether the results would generalize
to masters or grandmasters; second, it could be argued that this similarity
is more a reflection of the structure of the chess environment than of the
processes used by humans and computers—that is, any evaluation mechan-
ism allowing one to play chess well would correlate to some extent with the
evaluation functions used by Holding.
   Players have a hard time with the evaluation of pseudo-random positions
(Holding & Reynolds, 1982). These positions are ‘random’ with the con-
straints that no Pawn should be on the 1st or 8th row, no King should be
in check, and no piece attacked should be left without defence. Holding
and Reynolds first presented such positions for 8 s and asked players to
reconstruct them from memory. Then they restored the pieces, and asked
players to evaluate it. With such positions, there was no reliable correlation
between skill and memory or with the initial evaluation, neither was there a
correlation with a more informed evaluation judgement given by players after
analysing the position for several minutes. Yet, as we shall discuss later at
some length, there was a correlation between skill and the quality of the
chosen move.
   Holding (1985) proposes that evaluation skills, which are assumed to take
years to develop, are based on general principles, generic memory for typical
Pawn and piece formations, as well as episodic memory for events related
to one’s own and other players’ games. Given that the pseudo-random
positions used by Holding and Reynolds contain highly unfamiliar patterns
of pieces, these evaluation skills are not applicable. Players tended to ‘nor-
malize’ the positions during their search; that is, the positions at the leaves
of their search tree tended to converge to more game-like and familiar
positions. This behaviour is consistent with the idea that players use move-
selection and evaluation heuristics based on their experience, be they the
heuristics proposed by Holding or those proposed by others (e.g., Newell &
Simon, 1972).
   Holding and Pfau (1985) compared evaluations when imagining positions
to evaluation with full sight of the board at the end of the move sequence.
They dictated six moves from a position, and asked players to evaluate
the position after each pair of moves, using a numerical scale. Results were
clear cut for at least one of their three positions; both weak (< Elo 1500) and
strong (> Elo 1500) players reduced the difference between the final and
anticipatory evaluations as the imagined position became closer to the
final position. Moreover, the stronger players were always closer to the final
114   Moves in mind
evaluation. These results confirm that skilled players are better at evaluating
positions.
   Most of the results reported above were obtained with samples not con-
taining masters or grandmasters, but the overall picture is clear: stronger
players make better evaluations both in the base position and in the terminal
nodes of the search tree. This is consistent with the fact that strong
tournament players are usually good at speed chess, and that they can play
simultaneous chess against weaker opponents without losing much of their
superiority.


Reynolds’ homing heuristic
Newell and Simon (1972) and Wagner and Scurrah (1971) proposed principles
aimed at accounting for search behaviour. These principles, to which we will
return later in this chapter, are variations of what Newell and Simon (1965,
1972) called the win–stay and lose–shift hypothesis. That is, after positive
evaluations, players tend to deepen their search by homing onto favourable
lines and reanalysing the appropriate move sequence; after negative
evaluations, they tend to widen their search by considering alternative
moves. Reynolds (1982, 1991; see also Holding, 1985, pp. 198–200) tested the
hypothesis that skilled players tend to use this ‘homing heuristic’ more often
than weaker players. Thus, he expected that with skilled players (but not with
weaker players) search would narrow after positive evaluations, widen after
negative evaluations, and stay constant after neutral evaluations. Reanalysing
de Groot’s (1946) data for Position ‘A’, he found that grandmasters and
masters tended to increase the number of (base) moves considered after a
negative evaluation, to decrease this number after a positive evaluation, and
not to change it after a neutral evaluation. By contrast, Experts and weaker
players complied with the homing heuristic only with negative evaluations. It
is unclear as to what extent this result indicates intrinsic skill differences
in search behaviour (as proposed by Holding, 1985) or whether it is the
side effect of other skill-discriminating variables (such as the quality of
evaluations or the confidence placed in them).


Qualitative aspects of search in other board games

Selective search and move generation
Yoshikawa and Saito (1997a, 1997b) used an eye tracker for studying how
candidate moves are generated in Go. They found that players fixated between
stones, and not on them, a result that is similar to what has been found
with chess. Before making a move, they looked at only a small portion of the
board; after having made their move, they examined a larger area. Yoshikawa
and Saito also studied two players (2 kyu and 6-dan) solving tsume-Go
problems under time pressure. These are local ‘life-and-death’ problems,
                                     Problem solving and decision making   115
which are used as exercises for practising look-ahead abilities. The problems
were shown for 4 s. Eye-fixation recordings show that the strong player’s eye
fixations were fast (between 200 and 260 ms) for the problems he solved
correctly. Yoshikawa and Saito conclude that strong players identify good
candidate moves rapidly, unlike weaker players, who must rely on search in
order to find them.
   Mori (1996) studied the strength of the ‘aha!’ experience in shogi (Japanese
chess). The moves that were selected first in a problem-solving task resulted in
a weaker ‘aha!’ experience when correct than moves that were selected later.
Mori used tsumi-shogi problems, which, contrary to the more open-ended
problems used in chess experiments, have only one correct sequence of moves
to mate the King (see Figure 6.1).
   There is substantial evidence that the correct mental representation of a
problem simplifies its solution, sometimes dramatically, in domains ranging
from puzzle solving to scientific discovery (Kotovsky, Hayes, & Simon,
1985; Richman et al., 1996). Fu (1995) addressed the link between problem
representation and solution strategies, using the game of Hi-Q, a form of
solitaire chess. Experiments and computer simulations indicated that novices
generated three types of problem representation, which corresponded to




Figure 6.1 Example of the type of problem used by Mori (1996).
116   Moves in mind
three types of strategy: trial and error, concentration (moving the pieces from
the periphery to the centre of the board), and decomposition (moving the
pieces section by section). Fu suggests that the three representations reveal
different levels of cognitive structuration of the problem, and that the three
types of strategies differed in their selectivity and effectiveness.


Phases of move choice
Retschitzki (1989) interviewed a group of five strong awele players (adult
illiterate farmers in Ivory Coast) about eight game situations. The verbal
reports indicated a similarity with the type of reasoning exhibited by players
of other board games. According to their accounts, players never chose the
next move randomly. They analysed situations, and this process seems to take
the following steps: (a) identification of the characteristics of the situation
(threat, possible captures, move advantage); (b) choice of subgoals and
possible objectives according to the previous analysis (creation of a threat,
suppression of a threat, creation of a ‘kroo’, that is, accumulation of seeds in
a cup so that a capture would be possible in the second round); and (c) choice
of tactics with regard to these objectives. The final choice of the move to play
depended on a last reflection taking into account the possible consequences
of the different moves good enough to be considered. The players seemed to
use different means such as anticipation, hypotheses, deduction, a concept
of strategy, and the consideration of several techniques. Retschitzki thus
reached the conclusion that these illiterate players used formal thinking
during play (see also Chapter 7).


Evaluating positions
In their study of Go and gomoku, Eisenstadt and Kareev (1975) identify a
minimum of four evaluation strategies in search behaviour. Static evaluation
only assesses the position by examining the properties of the pieces involved,
while dynamic evaluation involves possible moves and countermoves as
well. Extrapolative evaluation concerns repetition on the board. Once the
repetition in the move sequence is realized, the remainder of the sequence
can be extrapolated. Finally, semi-dynamic evaluation also allows a rapid
sequence evaluation since in this case only the moves of one player need
to be evaluated. Forced moves are common examples of this evaluation
strategy. While these repetitious and forced moves are less common in
chess, games with obligatory captures such as checkers and bao have frequent
semi-dynamic evaluations. Eisenstadt and Kareev contend that pattern
recognition allows expert players to use static evaluation more often than
semi-dynamic or even dynamic evaluations.
   Bao experts use different evaluation times in comparison to chessplayers
(de Voogt, 1995). Contrary to chess, the evaluation times in bao are not
longer than 5 minutes in a serious match. This is not the result of speed
                                     Problem solving and decision making       117
play but constitutes a clear maximum in calculating skills. The difference in
evaluation times is the result of a difference in calculation speed that was also
attested in experiments.
   At the other extreme, we find Go, which has no clear limitations to
thinking time, as the latter is limited neither by volatility, as in bao, nor
by tournament rules, as in chess. It is therefore possible, if only in world
championship matches, that games last for more than a day. Evaluation
strategies in Go are based on patterns that have been difficult to quantify in
experiments. Clearly, more research in this field is necessary.


Use of strategies and rules
Cole et al. (1971) investigated malanj, the mancala game played by the Kpelle
of Liberia. They organized a tournament with 16 players and recorded
30 games. Following a brief analysis of these games, they highlighted the
diversity of players’ competences as well as the use of strategies and hypo-
thetical rules by the best players. Their style of play is described by Cole et al.
(1971) as:

    careful counting of seeds and setting up of captures, controlled by a
    strategy. Hypothetical rules (‘if I play the seeds from this hole, and if he
    responds by playing the seeds from that hole, then I can play the seeds
    from that other hole on the next move and win five seeds’) underlie all
    such captures. (p. 183)

   Four ‘strategies’ are described, which could better be called typical moves
or tactics: (a) waiting until the opponent had made the first capturing
move; (b) redistribution of forces; (c) tempting the opponent to make a
capture, which will prove in the long run unprofitable; and (d) keeping large
numbers of seeds in certain holes in the middle of his side of the board. Cole
et al. (1971, p. 184) conclude that victory in this game depends on a set of
strategies:

    The winning player makes sure he has solid defences, that he catalogues
    the possibilities of every move, that he reserves time to himself, that he
    lures the opponent into making premature captures, that he moves for
    decisive rather than piecemeal victories, and that he is flexible in
    redistributing his forces in preparation for new assaults.

Empirical data on the role of perception in problem solving
The role of pattern recognition in problem solving has been a recurrent topic
in this book. One method used to study this question is the recording of
eye movements, which has already been discussed in Chapter 4 on perception.
Here, we briefly review studies where this technique has been used in a
118   Moves in mind
problem-solving situation. As mentioned earlier, Tikhomirov and Poznyan-
skaya (1966) recorded the eye movements of a chess Expert while he was
choosing a move in a familiar middlegame position (the position was taken
from a game the participant had just finished). They found that their player
fixated on only a limited number of squares, focusing his attention on what
Tikhomirov and Poznyanskaya have dubbed the ‘orientation zone’. The
maximum number of eye fixations per second was four. Successive fixation
points yielded information about the location of men and squares that
may or may not have been associated with possible moves. Tikhomirov and
Poznyanskaya used these eye movements to identify the macrostructure of
the choice process, proposing the three stages that were described earlier.
   Simon and Barenfeld (1969) developed PERCEIVER, a computer pro-
gram simulating the initial eye movements of a chessplayer in a problem-
solving situation. PERCEIVER incorporated routines from MATER (Baylor
& Simon, 1966), a program specialized in mating combinations. In particular,
some of these routines specified chess relations between pieces, such as A is
attacking B, A is defending B, A is attacked by B, and A is defended by B.
   PERCEIVER was tested on Tikhomirov and Poznyanskaya’s (1966) data.
It moved its simulated eye around the board in good agreement with the
human data. In particular, the simulations supported two hypotheses for-
mulated by Simon and Barenfeld: (a) information gathered during the
first seconds relates to chess relations between pieces (mostly pairs of pieces)
or to relations between pieces and squares; and (b) when attention is fixed on
piece A, and a chess relation is noticed in peripheral vision which connects
A with another piece B, attention may either go back to A without a new
fixation, or be directed to B.
   Choosing Tikhomirov and Poznyanskaya’s data to test PERCEIVER was
unfortunate, because these eye movements were those of a player searching
for a move in a game he had just completed. The position was therefore
known to him. By contrast, PERCEIVER was intended to simulate the initial
fixations of a player confronted with an unknown position. Indeed, as we
have seen in Chapter 4, players’ eye movements rely less on relations of attack
and defence than was suggested by Tikhomirov and Poznyanskaya’s data. It
should be pointed out that, in this case, the players’ task was to remember a
briefly presented position.
   The data collected by Charness, Reingold, Pomplun, and Stampe (2001)
offer fresh light on the type of eye movements used when chessplayers
attempt to decide on a move in an unknown position. As expected, Experts
were faster than intermediate players and selected better moves. They also
needed fewer fixations per trial and their saccades showed greater amplitude.
Unlike de Groot and Gobet’s (1996) results, the two groups did not differ
with respect to the distribution of fixation durations. A detailed analysis of
the spatial distribution of the first five fixations indicated that Experts were
more likely to fixate on empty squares. In addition, when only the fixations
on pieces were considered, experts tended to fixate on relevant pieces more
                                   Problem solving and decision making     119
often than did intermediate players. Charness et al. (2001) concluded that
strong players encode chess patterns using perceptual chunks, and that they
use parafoveal or peripheral vision to identify important pieces and use this
information to guide their eye movements.


Empirical data on the role of knowledge in problem solving

Role of schemata and high-level knowledge
As noted in Chapter 3, the psychological importance of conceptual schemata
in board-game playing has been appreciated for a long time, at least in chess.
In all cases, and in particular with de Groot (1946), the importance of
schemata resides in the information made available in problem-solving situ-
ations. De Groot’s originality was to link schematic knowledge to perception:
Experts and masters perceive a position in ‘large complexes, each of which
hangs together as a genetic, functional and/or dynamic nature’; each complex
‘is to be considered as a unit of perception and significance’ (de Groot,
1946/1978, pp. 329–30; italics in original). Note that these complexes are
larger than the chunks that were later proposed by Chase and Simon (1973a,
1973b). De Groot also suggested that players’ descriptions of games are
centred on key positions of the game. Later research (e.g., Cooke et al., 1993;
de Groot & Gobet, 1996; Saariluoma, 1995) has confirmed the role of
conceptual knowledge in chess expertise.
   As discussed by de Groot and Gobet (1996), the relationship between
expertise, problem solving, and conceptual knowledge is complex. For
example, when chess masters annotate a game, they rarely argue logically
using clear-cut verbal concepts. Rather, they provide sequences of moves
punctuated by broad evaluations (such as ‘white has the initiative’ or ‘e5 is
a strong square’). De Groot and Gobet suggest that this may be due to the
lack of adequate terms describing chess concepts. While there is a rich and
well-differentiated vocabulary for describing openings, a similar language is
lacking for middlegames. Unlike artistic problem chess, competitive chess has
relatively few terms expressing combinations or positional features. De Groot
and Gobet give the example of a common Pawn structure in the French
defence that lacks any descriptive term. Interestingly, attempts to develop a
rich and precise terminology, like that of Kmoch (1980), were unsuccessful.
The same applies to computer chess: while it has been suggested several times
to develop high-level chess languages (e.g., Newell, Shaw, & Simon, 1958a),
such languages have not found wide acceptance. As a group, these observations
suggest that a representation based on a linear ordering is not appropriate for
chess, and that a visuo-spatial representation is more suitable. Two recent
papers may be mentioned at this juncture. George and Schaeffer (1991) have
suggested that a graphical, rather than verbal, interface may be a better
medium to elicit knowledge from experts, and Donninger (1996) has actually
implemented such an interface.
120    Moves in mind
   De Groot (1946) emphasizes that chess masters use stereotypical
knowledge and highlights the advantages offered by such knowledge. This
‘system of playing methods’, which includes tactical and strategic methods,
as well as opening theory, has been progressively constructed and refined
during chess history; each master, depending on his style, has acquired a
different combination of methods. The presence of such methods, many
of them reproductive, allows masters to play good chess without too much
look-ahead, simply by applying routine knowledge. Thus, playing chess does
not so much require the ability to discover new methods as to use old,
well-known methods efficiently. This hypothesis has been tested using tactical
problems as input. Saariluoma (1990, 1992a) showed that strong players
chose stereotyped solutions, even though shorter (but uncommon) solutions
were present (see Figure 6.2). Here, solution length was counted in the
number of moves to reach mate.
   Chessplayers’ knowledge seems to be specific to their domain of specializa-
tion, at least in part. Gruber and Strube (1989) compared experts in competi-
tive chess with experts in artistic chess composition (see Chapter 3). They
found that the composers were better and faster than the players at solving
artistic problems. (Gruber and Strube did not compare players and com-
posers in game situations.) These differences were reflected in the declarative
knowledge of the two types of expert.


Pattern recognition and search
As mentioned in Chapter 3, Chase and Simon proposed that pattern recog-
nition played an instrumental role in search behaviour. On several occasions
in the current chapter, we had the opportunity to present evidence supporting
their view. The role of pattern recognition in problem solving has also
generated criticism, a good summary of which can be found in Holding
(1985). In particular, Holding and Reynolds’ (1982) experiment is often taken
as evidence that search is dissociated from pattern recognition in chess. In this
experiment, which included players from novices to Experts, chess skill did
not correlate with the recall or evaluation of briefly presented semi-random
positions, but did correlate with the quality of moves proposed. According to
Gobet and Simon (1998b), Holding and Reynolds’ error in interpreting these
data in the light of the chunking theory is to assume that players use pattern
recognition only in the problem position, and not in the positions visited
during look-ahead search. But Chase and Simon (1973b, p. 272) were clear
that pattern recognition is applied recursively during look-ahead:

      When the move is made in the mind’s eye—that is, when the internal
      representation of the position is updated—the result is then passed
      back through the pattern perception system and new patterns are
      perceived. These patterns in turn will suggest new moves, and the search
      continues.
                                    Problem solving and decision making      121




Figure 6.2 Saariluoma elegantly demonstrated that chess knowledge can be strongly
           stereotyped. The ‘smothered mate’ in the top diagram is well known to
           chessplayers. When shown the bottom-left position, players propose the
           stereotyped sequence 1.Qe6+ Kh8 2.Nf7+ Kg8 (bottom right diagram)
           3.Nh6++ Kh8 4.Qg8+ R × g8 5.Nf7 checkmate, leading to the top diagram.
           However, 3.N × d8+ Kh8 4.Qe8 checkmate is shorter but not standard.
           (After Saariluoma, 1995.)

   As a consequence, a memory test solely on the initial problem position is
a weak method to test the recognition-association assumption. Schultetus
and Charness (1999) improved Holding and Reynolds’ (1982) experiment,
adding a crucial extension: they asked their participants to recall the position
following problem solving. In line with the original study, the quality of the
move chosen after problem solving, but not the initial recall of the position,
was related to chess skill. Significantly, recall performance following problem
solving was correlated with chess skill. For Schultetus and Charness (1999),
these results support the opposite view to that defended by Holding and
122   Moves in mind
Reynolds: pattern recognition underpins skill in chess. They suggest that
mechanisms such as long-term working memory retrieval structures
(Ericsson & Kintsch, 1995) or templates (Gobet & Simon, 1996c) could
account for the storage of semi-random positions during problem solving.
   As mentioned earlier in the section on selective search, there is some direct
evidence supporting Chase and Simon’s view. It is worth revisiting some of
this evidence here. World chess champion Gary Kasparov carried out a series
of simultaneous displays against several national teams and the strong
German team of Hamburg. In these matches, it was not uncommon for
Kasparov to face several grandmasters. Gobet and Simon (1996d) reasoned
that, as Kasparov played simultaneously against four to eight opponents, his
thinking time decreased accordingly. Although the matter is complicated by
the fact that pattern recognition occurs during look-ahead as well as during
the evaluation of the initial position, Gobet and Simon proposed that, if
search plays a predominant role in chessplaying, a large decrease in thinking
time should drastically reduce the level of performance; if, on the contrary,
pattern recognition is more important, a large decrease in thinking time
should have less effect, since better players would still keep an important
edge due to their ability to identify strong moves and key ideas rapidly.
Drawing on the Elo system as a measure of chess performance, Gobet
and Simon compared Kasparov’s strength in normal circumstances with
his performance when playing several games simultaneously. Kasparov’s
median performance in his simultaneous displays was only 100 points
below his strength with normal thinking time, which would still place
him among the six best players in the world at the time. This result was
taken as evidence for the essential role of pattern recognition. (See Gobet &
Simon, 2000b, and Lassiter, 2000, for discussion of this interpretation of
the data.)
   Chabris and Hearst (2003) analysed data from six editions of the Monaco
tournament, where top-level grandmasters played both rapid games (less than
30 s per move, on average) and blindfold games, played at about the same
speed but without the view of the position. They compared these results
with classical games (about 3 minutes per move, on average) between the
same players. In the three conditions, a strong computer program was used to
identify blunders; in general, blunders were defined as actual moves that were
evaluated at a minimum of 1.5 Pawn below the best move identified by the
program. Chabris and Hearst found that players committed more blunders
per 1000 moves in rapid games (6.85) and blindfold games (7.63) than in
classical games (5.02). The frequency of blunders was statistically sig-
nificantly smaller in classical games than in rapid and blindfold games,
but not smaller in rapid than in blindfold games. The same pattern of results
occurred with more stringent criteria for errors (difference larger than 3, 6,
or 9 Pawns instead of 1.5 Pawn), and when the magnitude of errors was
compared. Chabris and Hearst interpreted these data as opposing Chase
and Simon’s (1973b) view that pattern recognition is more important than
                                    Problem solving and decision making     123
search in expert chess. This conclusion is disputable, as Chabris and Hearst
incorrectly assumed that, in Chase and Simon’s theory, pattern recognition
occurs only with the initial candidate moves (see our discussion of Holding
and Reynolds’ experiment above); moreover, given that thinking time had
been cut by a factor of six, an increase of 1.83 blunders per 1000 moves does
not appear particularly large, as claimed by Chabris and Hearst.


Analogy formation in novice players
Most of this chapter concentrates on problem solving and decision making
with players having substantially more knowledge than novices. Several
researchers have addressed these questions from a different angle: how do
novices learn the regularities of a board game? Didierjean, Cauzinille-
Marmèche and Savina (1999) were interested in how chess novices use
reasoning by analogy in learning to solve chess combinations (smothered
mates). They were first presented with examples of problem solutions, and
then showed positions similar to the original examples. The results show that
transfer was limited to problems perceptually similar to the examples. Thus,
novices only used knowledge that had a low degree of abstraction.
   Marmèche and Didierjean (2001) expanded the previous study by inducing
two modes of problem encoding. In one group, the explanations focused on
the sequence of elementary solving steps; in the other, the explanations
related to the general principle for solving the class of problems under study.
Participants then attempted to solve problems that were similar either at a
superficial or an abstract level. Finally, there was a recall test on the first
problem. Again, results indicated that knowledge generalization is conser-
vative—that is, many participants, in particular in the group receiving only
the sequence of moves, could not solve the problem requiring the abstract
principle. Participants who were able to generalize their knowledge were
also better at memorizing context-dependent elements. Marmèche and
Didierjean conclude that the acquisition of problem-solving skills involves
the construction of different types of encoding, including perceptual and
abstract encoding, which evolve in parallel.


Theoretical accounts
As has become obvious in the preceding pages, much is known about the way
in which individuals play and make decisions in board games. Consequently,
a number of theoretical proposals have been advanced. Before considering
how the empirical results presented in this chapter relate to the main theories
of expertise discussed in Chapter 3, we briefly review two artificial-intelligence
models of search that are of interest to psychologists, and discuss a few
psychological models specifically developed to account for empirical data on
problem solving.
124   Moves in mind
Artificial-intelligence models relevant to the psychology of search
Two chess-playing programs, written by Pitrat and Wilkins, respectively, were
developed to capture some features of human search, such as selectivity.
Pitrat’s (1977) program operates in two stages. First, it analyses the position
in order to identify favourable configurations; second, it constructs plans and
tries to apply them. Four goals are taken into consideration: piece capture,
double attack, attack against the King, and Pawn promotion. If these plans
fail, the program carries out a deeper analysis of the position, and then
generates new plans that attempt to correct what was wrong in the previous
ones. This behaviour can be compared to human progressive deepening
(de Groot, 1946). The program generates only branches that are natural,
which allows it to cut the search tree down to the same size as humans’
(around 100 positions). It could find combinations requiring up to 20-ply
search, and performed well in a series of combinations leading to checkmate
or to material gain. Contrariwise, the small number of plans and heuristics
used by the program did not enable it to play entire games at a reasonable
level.
   PARADISE (PAttern Recognition Applied to DIrecting SEarch) was
developed by Wilkins (1980). Like Pitrat’s program, PARADISE’s domain
covers tactical middlegame combinations. Knowledge is encoded as pro-
duction rules (about 200). The condition part of these productions matches
board patterns, and actions update working memory. Productions have two
main uses: discovery of plans during static analysis, and verification of the
chosen move. As PARADISE does not limit its depth of search, it was able to
solve problems requiring a search of up to 20 ply. In general, the magnitude
of the search trees it developed was similar to that of humans’. In its domain
(tactical middlegames), PARADISE played near the Expert level.


Psychological models of search in chess
Several models have been proposed to account for search behaviour in chess.
(To our knowledge, no model has been developed for other board games.)
In the conclusion of this chapter, we will take a broader view and evaluate
theories integrating search and pattern recognition in problem solving.


Models of selective search and principles of search
The idea that heuristics enable selective search was implemented in two com-
puter programs (see also Chapter 3). With NSS (Newell, Shaw, & Simon,
1958a; Newell & Simon, 1972), behaviour is directed by a set of goals. Two
move generators operate to fulfil these goals, one for base moves and one
for moves occurring during the analysis of a branch. NSS satisfices, that is,
chooses the first moves that reach a given value. While NSS’s playing strength
was limited, its search was highly selective. MATER (Baylor & Simon, 1966)
                                   Problem solving and decision making     125
also used a small search space. It restricted its search to forced moves, and
to variations with few responses by the opponent. MATER was strong in
mating combinations, but limited to that domain.
   Based on the analysis of verbal protocols, Newell and Simon (1965, 1972)
proposed six principles governing the generation of episodes and moves:

 1 The analysis of each base move (move in the stimulus position) is
   independent of the analysis of other base moves.
 2 The first episode with a base move uses normal moves, while in later
   episodes, more unusual moves are selected.
 3 If the evaluation of an episode is positive, the analysis of this episode is
   continued. If not, a new base move is investigated.
 4 During the exploration of variations, there is a tendency for the moves
   chosen by the opponent to be favourable to the player. This bias limits
   the search space.
 5 The analysis of a base move is given up in favour of another move
   discovered during the episode, if the latter seems more profitable to the
   player or to his opponent.
 6 Before making the final choice, the alternative base moves are tested.

   De Groot’s (1946) protocols strongly support the first three principles,
but only weakly the last three. Principle 3 was also verified by Reynolds’
(1982, 1991) reanalysis of de Groot’s data. By contrast, Wagner and Scurrah
(1971; Scurrah & Wagner, 1970), who analysed search behaviour of a single
participant in a number of middlegame and endgame positions, found that
principle 3 was often violated, in particular with negative evaluations (the
player tended to persist with the current move, rather than to shift to a new
one). Wagner and Scurrah proposed further rules to take care of these new
results.
   During problem solving, players periodically attempt to re-evaluate the
problem. This re-evaluation is formulated in general terms, and its validity is
not specifically tested afterwards. Newell and Simon (1965) propose several
explanations for this re-evaluation. It may be due to the discovery of a new
aspect of the position, which was neglected before; to the realization that a
move did not turn out as expected; or to the fact that the analysis of a base
move produced results different from those expected.
   To sum up, Newell and Simon (1965) essentially drew the same conclusion
as de Groot (1946): chess skill derives mainly from pattern recognition and
the use of heuristic rules, both of which are learned through practice and
study, and enable a highly selective search.


CHUMP and SEARCH
While Simon and his colleagues developed various computer models of
problem solving in chess in the 1960s, none of them directly incorporated
126   Moves in mind
the recognition-association mechanism of the chunking theory. Gobet and
Jansen (1994) proposed CHUMP (CHUnks and Move Patterns), a program
using pattern recognition to select moves; conversely to the models of Simon
and colleagues, the program did not carry out search. A probabilistic model
integrating both mechanisms was recently proposed by Gobet (1997a). The
model, called SEARCH, does not play chess per se, but computes a variety of
behavioural measures, such as depth of search, rate of search, and the level
of fuzziness in the mind’s eye. The model is an implementation of the
template theory. Moves can be generated either automatically (proposed
by chunks and templates) or through heuristics. Similarly, position evalu-
ation at the end of a sequence of moves is done probabilistically, either
automatically or through heuristics. The generation of an episode is ended
when one of the following three conditions apply: the level of fuzziness in the
mind’s eye is too high; an evaluation has been proposed; or no move or
sequence of moves has been proposed. Finally, the model includes assump-
tions about the rate of decay in the mind’s eye, which hampers search. Every
cognitive operation is associated with a time cost. For example, it takes 2 s to
carry out a move internally, and it takes 10 s to compute an (nonautomatic)
evaluation.
   Figure 6.3 gives a flowchart of SEARCH. As we have seen earlier, the
program predicts that depth of search follows a power law of the skill level,
contrary to Charness’s (1981a) assumption that depth of search levels off at
high levels of skill. Gobet (1997a) suggested that Saariluoma’s results, where
international masters and grandmasters searched less than weaker masters,
are actually compatible with SEARCH’s prediction that depth of search
follows a power law of skill. This is because of the variability inherent to the
simulations and the small number of participants in typical chess research.


Discussion
Choosing good moves is the essence of board-game playing. Thus, the evi-
dence reviewed in this chapter is crucial in evaluating the theories presented in
Chapter 3. When presenting these theories and applying them to empirical
data about perception and memory, we noted that they all emphasized
both knowledge and search, although they weighted the two components
differently. We can now evaluate more critically their ability to explain how
players solve problems and make decisions. To simplify the discussion,
one can classify these theories into two broad categories: informal theories,
which were only formulated verbally, and formal theories, which were also
embodied in computational models.


Informal theories
Most of the theories we have considered belong to the first group. Some, like
Binet’s theory, say little about problem solving. Others explicitly deal with it,
                                  Problem solving and decision making   127




Figure 6.3 Flowchart of SEARCH.

but offer few details about the mechanisms involved. Prime examples are
Cleveland’s and Holding’s theories. While both incorporate concepts from
general problem-solving psychology, neither makes clear-cut predictions.
The remaining informal theories provide a wealth of detail, and thus merit a
detailed discussion.
128   Moves in mind
   De Groot’s (1946) approach is anchored in Selz’s (1922) theory of pro-
ductive thinking, which proved fitting for describing the structure of verbal
protocols, including the three phases of problem solving. It was also germane
to the concepts—such as methods, heuristics, and decision strategies—that de
Groot used to describe problem solving. One aspect of Selz’s theory that was
not borne out by the data was the prediction of clear-cut skill differences in
the structure of thought. Thus, thinking methods differ across skill levels by
their contents, but not by their structure. From the point of view of modern
cognitive psychology, the Selzian heritage apparent in de Groot’s theory
had the consequence that this theory was essentially descriptive, and did not
specify the mechanisms underlying players’ behaviour. To this charge, de
Groot would retort that, even now, it might be too early to postulate such
mechanisms (see, for example, the final chapter of de Groot & Gobet, 1996).
   While empirically productive, Tikhomirov and his group did not crystallize
their results theoretically. Their approach, which combines emotion, moti-
vation, and cognition to account for problem solving, appears abstract and
underspecified. Its strength lies more in offering a descriptive vocabulary than
in providing explanatory mechanisms. In particular, the proposed theories
are hard to test experimentally.
   Like the previous two theories, Saariluoma’s approach has this flavour that
clearly distinguishes between continental and Anglo-Saxon psychology.
To explain problem solving in chess, Saariluoma uses Leibniz’s concept of
apperception—a terminology that may appear confusing to some. Similarly,
Saariluoma’s emphasis on contents analysis may seem alien to some readers:
if one wants to understand a domain of expertise such as chess, there is no
escape from studying the nitty-gritty of chess combinations, endgames, and
technique in general. The necessity of contents analysis raises important
questions on how to study board-game psychology, an issue we will take
up at the end of this chapter. The strength of Saariluoma’s approach is to
have combined a deep theoretical reflection with crisp experimental manipu-
lations, perhaps placing more emphasis on generating new phenomena than
testing theoretical details.
   Information-processing theories catered for a different style than the
approaches we have reviewed so far. Simon always had a strong inclination
for formal theories and a certain disdain for verbally formulated theories
(e.g., Newell & Simon, 1972; Simon, 1947). Compared with the previous
approaches, Simon’s models may appear at first sight simple, if not naïve. The
reason for this is that they typically addressed only one aspect of expertise—
perception of a new position, memory for game positions, or solving mating
combinations—with the aim of producing clear experimental designs, and
developing detailed computational models.
   Ironically, Simon’s most influential theory of expertise, the chunking
theory, is relatively underspecified by his own standards. This does not pre-
vent it from making precise empirical predictions. As we have seen, Chase
and Simon (1973b) expanded their theory, originally developed to explain
                                    Problem solving and decision making     129
memory data, to the realm of problem solving by proposing that chunks
are used as conditions of productions. Recognition of chunks gives access
to stored information, and recursive application of productions makes
it possible to conduct search in the mind’s eye. Several empirical results
follow directly from these mechanisms, such as Saariluoma’s (1992a) data
suggesting stereotyped behaviour (at least in simple problems), de Groot’s
(1946) evidence for selective search and forward search, and the necessity for
progressive deepening (due to limits in memory).
   The chunking theory also accounts for the fact that, with routine problems,
experts can often find a solution by recognizing features of the problem at
hand, while novices have to carry out more search. With such problems,
the rapid understanding sometimes known as intuition may be equated
with pattern recognition. More complex problems reduce the likelihood
that similar problems and their solutions had been encoded with sufficient
detail in the past, and recognition of features is not enough. In this case,
problem solvers must fall back on more search, guiding their exploration
with both the information at hand and that provided by the goals that
may have been identified. Finally, the recognition mechanisms incorporated
in the chunking theory also emphasize the key role played by knowledge. This
includes knowledge enabling the accurate and rapid evaluation of positions.
Thus, despite Holding’s (1985, 1992) conclusions, the correlation between
skill and the ability to evaluate positions follows directly from chunk-based
theories.
   Most of what we have said about the chunking theory also applies to the
template theory, which is an outgrowth of the chunking theory. The presence
of templates accounts for some more phenomena, such as the type of macro-
search found in chess, where players reason from typical positions to other
typical positions without explicitly mentioning the operators (sequence of
moves) (Charness, 1981b; Saariluoma & Hohlfeld, 1994).


Formal models
The strength of formal theories in psychology is that they are explicit about
the cognitive structures and mechanisms involved. Their weakness is that, to
satisfy this first requirement, they have to ignore several details to focus on a
few selected aspects of reality. As is clear from the previous sections, the
majority of the formal models discussed in this chapter have been influenced
by the work of Simon.
   Newell and Simon (1965), as well as Wagner and Scurrah (1971), presented
principles aimed at explaining the transition from one episode to the next
during search. To some extent, these models are descriptive; they are also
devoid of content, only the surface structure of the protocols being taken
into account. SEARCH (Gobet, 1997a) formalizes the way search is con-
ceived in the template theory. While mechanisms for generating moves are
specified, which is an improvement on the models just mentioned, the model
130   Moves in mind
also lacks content: it does not really play chess: it ‘just’ makes predictions
about variables such as depth of search. Content is present in some early
artificial-intelligence models, such as Wilkins and Pitrat’s production
systems, NSS, and MATER. Unfortunately, these programs, while showing
that the provision of heuristics can make selective search possible, were
limited to a subset of the game. Moreover, when a comparison was carried
out with human data, this typically was done qualitatively only.
   As we shall see in the next chapter, models, typically using production
systems, have also been used to account for developmental aspects of
problem solving in other games, such as tic-tac-toe and awele. In general,
the more complex the game, the harder it is to even approximately emulate
human behaviour.


Conclusion
Several programs have fulfilled artificial intelligence’s old dream of beating a
reigning world chess champion in a board game (see Chapter 2). By contrast,
the state of the art in board-game psychology is less advanced, and we are
far from having developed simulation models that closely replicate human
problem-solving behaviour along a variety of dimensions. Just as empirical
research into problem solving seems to lag behind that into memory,
simulation models of search and decision making have not yet reached the
sophistication of models of memory. One possible reason for this difference is
that, as noted by Saariluoma (1995), understanding problem solving requires
research dealing with the content of the domain, which in turn calls for
researchers having a fair amount of expertise in this domain. This require-
ment seems less strict in the case of memory research, where experimental
manipulations and simulation models can be devised in spite of a superficial
knowledge of the game in question.
   While this situation indicates that our understanding of problem-solving
mechanisms is still wanting, it should not lead to gloomy conclusions about
research into board games. Indeed, fields like the psychology of reading,
language acquisition or mathematics, to take only fields with strong eco-
logical validity, have attracted more researchers than the psychology of board
games. But in none of these cases is there a computational model that reads,
acquires language, or does mathematics at a level even remotely related to
that of humans. Thus, compared with the current state of psychology in
general, theories of board-game psychology fare well, even in the case of
problem solving.
   The difficulty of developing theories that account for the full gamut of
skills necessary to play (complex) board games at a high level may explain
why board games may have been such a good choice to understand the
human mind. While no full answer has been given to characterize the
development and maintenance of these skills, there is no doubt that steady
progress has been made.
                                 Problem solving and decision making   131
  In this conclusion, we have given a rather detailed evaluation of the
theories at hand, in part due to the key role played by problem solving
and decision making in board games. Another reason is that the following
chapters will often deal with topics that are less directly linked to these
theories of expertise.
7      Learning, development,
       and ageing




The notion of change is at the heart of board-game playing. With every move,
the situation on the board is modified, sometimes drastically, as in bao or
awele. Change also affects players, through learning and development. Learn-
ing can be defined as change in explicit or implicit knowledge that affects
one’s behaviour. Development also has a biological connotation and refers
broadly to a sequence of changes over years. Both terms are ill defined in the
literature, and it is often difficult to classify empirical studies unambiguously
under one of these labels. Studies with adults tend to involve more learning,
although the effects of ageing start to affect performance from early adult-
hood onwards. Studies with children tend to deal more with development,
although it is often impossible to partial out the effect of learning.
   We begin this chapter with learning. We do so because this line of research
often refers to the chunking theory, and so the transition from the previous
chapters is straightforward. We then deal with research into development,
where the influence of the Swiss psychologist Jean Piaget will be dominant.
We end this chapter with a review of the data available on ageing.


Early stages of learning
To date, research into expertise has been mostly focused on the higher skill
levels. Relatively little is known about the first stages—including the beginner’s
stage—in the acquisition of expert behaviour. This is unfortunate, as the first
few hours of learning can be highly informative about the mechanisms
involved in acquiring a skill. In this section, we review the available evidence,
starting with chess. (A few more studies will be discussed in the section on
development.)


Learning the rules of pseudo-chess
Fisk and Lloyd (1988) studied the way novices learn how pieces move in a
pseudo-chess environment. Subjects saw a board with six pieces, represented
as letters, and a target T, and had to decide which piece could take the target.
Results showed a typical power law, with rapid speed-up in reaction time
134   Moves in mind
and decrease in the number of errors at the beginning followed by slower
improvement thereafter. After a few hours, the subjects were as fast as inter-
mediate-level chessplayers, but slower than masters. The presence of this
learning curve, which has also been found in other domains (Newell &
Rosenbloom, 1981) and which we will meet in other experiments on early
learning, could provide an explanation of why so many years of practice are
needed for an amateur to become a master: after a rapid learning phase,
improvement becomes slower and slower. This means both that further pro-
gress will require a larger investment of time and energy, and that high levels
of motivation must be sustained to enable this investment.


Training novices to memorize chess positions
Ericsson and Harris (1990) trained a novice to the point where she could recall
briefly presented game positions to the standard of masters. Performance on
random positions did not reach that of masters. (Note that in this study, as
in the following two, the participants did not learn to play chess, but simply
to memorize positions.) Saariluoma and Laine (2001), extending Ericsson
and Harris’ (1990) study, had two novices learn a set of 500 positions over
the space of a few months. The participants were tested intermittently with
a brief (5 s) presentation task, in which they had to recall 10 game and 10
random positions. The results showed a clear improvement in percentage
correct, from about 15 to 50% for game positions. The learning curve
also looked like a power function, as found by Fisk and Lloyd for skilled
visual search, with the greatest recall percentage increase within the first
100–150 positions learned. In addition, a slight increase was seen in the recall
of random positions.
   Saariluoma and Laine (2001) compared their human data to two computer
models. Their aim was to differentiate between two methods of constructing
chunks, both emphasizing a flat (as opposed to hierarchical) organization
of chunks in LTM. From their simulations, they concluded that frequency-
based associative models fit human data better than those based on spatial
proximity of pieces. However, Gobet (2001a) showed that CHREST, which
uses a proximity-based heuristic for chunk construction, accounts for
Saariluoma and Laine’s human data equally as well as their frequency-based
heuristic. CHREST also accounts for the increase found with random
positions.
   Gobet and Jackson (2002) obtained further data about how novices
learn chess positions. Their study improves on Saariluoma and Laine’s in
three ways. First, the two participants were selected on the criterion that they
were as ignorant of chess as possible. Second, they were tested after every
position in the learning phase. Third, presentation and reconstruction of
positions was done on the computer, which allowed precise and detailed data
collection. In particular, this made it possible to record latencies in piece
placement, which were used to infer chunks.
                                      Learning, development, and ageing    135
   The novices were trained to memorize positions over the course of 15 one-
hour sessions. As in the previous studies, increase in recall performance and
chunk size was captured by power functions. Evidence for the presence of
templates was also found. The human data were compared to those of a
computer simulation run on CHREST. The aim was to see whether a compu-
tational model that had been well validated with experts’ data could also
account for novices’ data. The model accounted for the human data,
although it tended to underestimate the size of the largest chunks and the rate
of learning.


From amateur to master
If little is known about how beginners learn to play chess, even less is known
about the progression from amateur to professional. The only longitudinal
study we found was that of Charness (1989), who studied the same chess-
player, DH, twice. This player, who had participated in several experiments
described in Charness (1981b, 1981c), was retested with the same material
nine years later. During this interval, DH’s rating increased from about
Elo 1600 to about 2400—an increase of four standard deviations. In
comparison to the first test, some patterns emerged clearly in the second.
In problem-solving tasks, DH was faster in choosing a move and explored
fewer different base moves (i.e., he was more selective). He was also quicker
in the evaluation of endgame positions and was somewhat more accurate.
However, the size of his search tree did not change much (it was actually
slightly smaller on the retest), neither did his maximum depth of search. In
the recall task, DH, who had already performed well in the first testing
session, achieved perfect recall 9 years later. In the second testing session,
chunks were fewer and larger, and the between-chunk latencies were smaller.
Charness takes this reduction in latency as an indication that DH used
hierarchically organized chunks.
   These results are consistent with the predictions of the chunking and tem-
plate theories, but do not support theories emphasizing search (e.g., Holding,
1985): increase in skill occurs mainly through differences in chunking
(increase in the size of chunks, speed in accessing chunks, increase in selec-
tivity), and not through an increase in search mechanisms (no change in the
size of DH’s search tree or in his maximal depth of search). Note that DH’s
chunk size in the retest (2.7 pieces, on average) was smaller than predicted
by the template theory; this discrepancy may be explained by the recording
technique used, which was similar to Chase and Simon’s (1973a, 1973b; see
Gobet & Simon, 1998a, and Chapter 5 of this book, for discussion).
   Another approach to estimate masters’ career path is to use retrospective
questionnaires about how much time they have spent doing chess-related
activities. Two studies have done this with samples ranging from weak
amateurs to grandmasters, taking as a framework the theory of deliberate
practice (Ericsson, Krampe, & Tesch-Römer, 1993). Deliberate practice
136   Moves in mind
consists of activities deliberately designed to improve performance; these
activities are assumed to be effortful and not enjoyable. This framework was
influenced by Simon and Chase’s (1973) estimate that masters have spent
from 10,000 to 50,000 hours playing or studying chess, while class A players
have spent from 1000 to 5000 hours. The proponents of deliberate practice
(e.g., Ericsson et al., 1993; Ericsson & Charness, 1994; Howe, Davidson,
& Sloboda, 1998) reject the existence of innate cognitive talent in expert
performance and propose that, in several domains including arts and sports,
the more skilled simply engage in more deliberate practice.
   Charness, Krampe, and Mayr (1996) tested this theory by asking 158
chessplayers from Canada, Russia, and Germany to report the number of
hours spent studying chess alone as well as spent playing or analysing
games with others. The estimated cumulative amount of deliberate
practice accounted for about 50% of the variance in skill. It was also
found that the number of hours studying alone, rather than the number of
hours studying and practising with others, was the best measure of deliberate
practice.
   Campitelli and Gobet (2003) aimed to test predictions from both the theory
of deliberate practice and Geschwind and Galaburda’s (1985) biological
theory of talent (see Chapter 9). About 100 Argentinian chessplayers filled in
a questionnaire measuring deliberate practice, starting age, and handedness.
The study replicated the importance of deliberate practice for reaching high
levels of performance (about 40% of the variance in skill accounted for),
but also indicated a large variability. In particular, the slowest player needed
seven times more practice than the faster to reach master level: an estimated
23,600 vs. 3200 hours. A correlation was also found between skill level
and starting age. (See Chapter 9 for the results about handedness.) Unlike
Charness and colleagues’ sample, the Argentinian results indicated that
group practice was more important than individual practice. Finally, the
number of speed games played was a good predictor of skill.
   De Voogt (1995) suggests that the location of the players is relevant to
mastership but not because of literacy, economy, or age. Rather, competition
is necessary to increase playing levels. When the best bao clubs in Zanzibar
were located upcountry, the best players were likely to travel there and meet
the players at the clubs, but when a number of clubs started to grow in the
city of Zanzibar and Dar es Salaam, this rapidly changed since the number
of players and competitions in the city would outgrow those upcountry. The
number of masters in a certain region was directly related to the number and
quality of clubs in that region.


Learning pegity and gomoku
Pegity is a variant of gomoku where the two players try to construct an un-
broken line of five pieces vertically, horizontally, or diagonally by alternately
placing one piece on an empty square of the board. The first empirical study
                                      Learning, development, and ageing    137
of this type of game was done by Rayner (1958a, 1958b), who observed a
large number of games played by adults and children between the ages of
5 and 15. He recorded various behavioural measures when these novices were
playing together in a tournament (25 games each). Having recorded each
move, Rayner was able to calculate several values showing the evolution with
age and experience: mean time per move, number of moves per game, etc.
He also classified the moves according to strategies (attack, defence, etc.).
Although the observation period was short, Rayner identified several changes
in strategy. For example, subjects learnt to parry more attacks from their
opponents, and they were able to achieve more of their own attacks. They
also learned typical sequences of moves. Finally, there was a strong tendency
to bias their attention toward their own moves (generally, attacking moves),
as opposed to anticipating the opponent’s threats.
   Kareev (1973) conducted a study in which 10 participants played gomoku
against a computer for 3 to 16 hours. Half of the participants were assigned
to a ‘without-options’ condition, and the other half to a ‘with-options’ con-
dition; in the latter case, participants had the opportunity to look back at
previous moves and to preview future moves. The results demonstrated the
existence of familiar patterns and their importance in suggesting possible
moves. Most participants were able to improve their level of play through
their interaction with the computer. Kareev proposed a model describing
game playing behaviour in three major stages: (a) learning the rules of the
game; (b) playing the game (generating moves); and (c) learning to play
a better game. Kareev argues that ‘the fact that even beginners do not play a
random game is attributed to the existence of so-called “primitive strategies”
which are assumed to be generated when the rules of the game are learned’
(Kareev, 1973, p. i). Unfortunately, Kareev did not analyse the difference
between the without-option and with-option conditions.


Learning: Conclusions
In comparison with memory, for example, there is relatively little research
about the early stages of learning in adults, particularly for complex games
such as chess or Go. The few additional studies we will consider in the section
about development will not force us to change this conclusion. Even so, a few
recurring themes may be identified. In several experiments, it was apparent
that learning follows a power law; this result is suggestive, because this
curve has been found in a number of experiments about learning as well
as in several school activities, such as learning arithmetic or programming
(Anderson, 1990a). Thus, it is at least plausible that common mechanisms
underlie learning in all these domains. The idea of perceptual chunking and
of coordinating strategies and concepts was highlighted in several studies
(e.g., Rayner, 1958a, 1958b), and will be a constant topic of discussion in the
following section on development. Coordinating information is obviously
what the chunking theory is designed to explain, and it is interesting that
138   Moves in mind
the same mechanisms used by CHREST to explain expert behaviour can also
account for the early stages of expertise—at least for memory. Charness’s
longitudinal single-subject study suggests that chunking mechanisms are
also consistent with the pattern of results found in problem solving. Even so,
the conclusion that we know little about how novices’ skills develop into
experts’ skills is hard to escape.


Development of play and game behaviour
As has already been mentioned, the classification of studies under the
headings of learning and development is somewhat arbitrary. Nevertheless,
the distinction is justified, for two reasons. First, studies dealing with develop-
ment investigate change in children, while studies of learning deal mainly
with adults. Second, researchers typically use a different theoretical frame-
work in the two cases; in particular, research on development has often
referred to Piaget’s theory. Given that this section will often draw on Piaget’s
conception of play and games (see Chapter 3), it is appropriate to pause and
situate developmental board-game studies in the context of research into play
more generally. After dealing with Piaget’s studies on play, we will consider
the developmental evidence with respect to a variety of games.

Piaget’s conceptions of play
Piaget (1945) described the development of play using three major categories:
practice play, symbolic play, and games with rules, which he associated
primarily with sensorimotor, preoperational, and operational intelligence,
respectively. For our purposes, games with rules are the most interesting
category. They consist of games of physical coordination (chase, marbles,
or ball games, etc.) and intellectual games (cards, chess, etc.). Both types
of game involve competition between individuals (without which the
rules would be pointless) and are regulated either by a code passed on
from generation to generation or by temporary agreements (Piaget, 1945,
pp. 151–3). These categories should not be considered as stages, mainly
because when a new form of play appears, older forms still remain available.
As an example, Piaget argued that even adults still behave in practice-play
fashion: when they buy a new car, they test it just to discover its new functions
and performance (Piaget, 1945, p. 121).
   According to Piaget, the evolution of these play behaviours can be
described in terms of peaks. Practice play peaks in the first 2 years, and then
diminishes with age (in absolute as well as in relative terms). Symbolic
play peaks between 2 and 4 years, followed by a similar decline. Finally, the
prevalence of games with rules tends to increase (relatively and absolutely)
with age. Eifermann (1971) conducted a study to test this hypothesis. Observa-
tions of several thousand Israeli children from grades 3 to 8 confirmed that
participation in symbolic play decreased, while participation in games with
                                      Learning, development, and ageing    139
rules increased from 6 to 10 years. Interest in games with rules declined after
the age of 10.
   Piaget also described a fourth category, ‘constructive play’, which consists
in the manipulation of objects to construct or to create something; construc-
tive play does not fall within a given stage of intelligence. Instead, Piaget
suggested that constructive play occupies a position halfway between play
and adaptive intelligence, because it could be considered as a ‘move away
from play in the strict sense, towards work, or at least towards spontaneous
intelligent activity’ (Piaget, 1962, p. 109). Studies done in preschool and
kindergarten classrooms have shown that constructive play is the most
common form of activity in such settings (Rubin, Fein, & Vandenberg,
1983), although observations carried out in playgrounds or at home might
have yielded a different picture.
   As a means of investigating moral judgements in children, Piaget
(1932/1965) analysed the rules of a boys’ game (marbles) and a girls’ game
(hide-and-seek), and tried to find out how they are played and perceived by
children. Piaget traced the consciousness of rules as it develops in children
through four stages. In the earliest stage, the rules are elaborated more or
less individually, and are influenced by a drive to repeat. In the second stage,
the actions of older children are imitated; children believe that they are
following rules, but, in fact, they continue playing individually. In the
third stage, social cooperation begins, and the rules are actually followed.
Finally, in the fourth stage, children consider the rules as the product of
mutual agreement, and are interested in rules for their own sake. In this
study, Piaget’s principal focus was the conception of and respect for rules.
He focused on the game of marbles because he was mainly interested
in spontaneous development and considered such a game to be a social
institution, where the rules are transmitted from one generation of children
to the next without adult intervention. This characteristic is not attested in
board games.
   Using Piaget’s categories, Parker (1984) presents an evolutionary perspec-
tive on human games. According to her, most games with rules fall into one
of four categories: field games, floor and table games, iconic games, and word
games. Board games and card games are the two subcategories of iconic
games. With regard to the cognitive demands of the various board games,
Parker argues that children understand the concept of rules when they enter
the concrete operational period, at about 6 years of age, even if they some-
times forget specific rules or change them during play. They also understand
the concepts of winning and losing. But they only apply rules consistently
when they enter the formal operational stage, at 11 or 12 years of age. More
precisely, she notes that ‘the iconization of contests and territorial invasion
is an interesting expression of the interiorization of reversible actions
characteristic of concrete operations’ (Parker, 1984, p. 281). With respect to
card games, she states that ‘scoring in these games typically requires the
concrete operational ability to classify objects simultaneously according to
140   Moves in mind
two criteria . . . and the formal operational ability to calculate probabilities’
(p. 282).
   Sutton-Smith (1976) has created a ‘structural grammar’ for analysing game
collections. The grammar is based on Piaget’s theory of cognitive develop-
ment. Sutton-Smith first distinguishes four systems of regulation corre-
sponding to prescriptive games, central-person games, competitive games,
and sports; the entire system has seven levels, each higher level corresponding
to a shift in the logical operations underlying the game and an increase in
organizational complexity. Applying the grammar to several North American
game collections, Sutton-Smith (1976) reports an association between the
level of the games played by children and their presumed level of cognitive
development based on their age.
   Sutton-Smith and Roberts (1981) suggest that there exists a psycho-
logically ‘universal competence to games’. This competence, like that of
linguistic competence, is an integral part of the human condition. The fact
that it is not used much by some tribal groups such as pygmies does not mean
that it is absent. Sutton-Smith and Roberts (1981, pp. 447–8) see game playing
‘as a generative social procedure whereby oppositions between people, or
within a person, are transformed into a set of alternating ludic behaviours.
Games in these terms are a cognitive-social device for managing conflict’.
   Lancy (1984) studied the games played by children in 10 societies of
Papua New Guinea. He had to develop a new system because Sutton-Smith’s
grammar was not broad enough to analyse the games found in these groups.
Lancy identified eight attributes that can be used to estimate game complex-
ity. He found only weak correlations between features of play and cognitive
development as measured by a battery of cognitive tests.


Children’s preferences
Using a play inventory, Sutton-Smith and Roberts (1967) carried out a survey
of children’s game preferences. These data, based on a large sample of
American children, indicate that board games are not children’s first choice.
While 70% of the children reported knowing tic-tac-toe, this game ranks only
in the middle of the preference scale for grade-3 to grade-5 children. Checkers
appears a bit lower in the ranking, but is more popular with eighth graders,
where only some girls still mention tic-tac-toe. Cards and Monopoly are only
cited in the top 30 play activities by older children (grades 6 to 8). Opie and
Opie (1969) conducted a similar study of British children’s leisure activities.
They found that children preferred their own games over adult-directed
games and even games learned directly from other children.


Developmental studies of specific board games
After this broad introduction to the relation between games and develop-
ment, it is time to look into studies of specific board games. We will divide
                                       Learning, development, and ageing     141
these studies into two groups: elementary games and complex games. To
distinguish between them, we adopt the criterion of being able to discover
a winning strategy (or a way of not losing) after playing a few games. We will
discuss the studies within each group in roughly chronological order.


Elementary games

Pegity (gomoku)
As noted above, Rayner (1958a, 1958b) compared the performance of
children between the ages of 5 and 15 with that of adults. Special attention
was paid to changes that took place between the ages of five and seven. Five
year olds played most games in the minimum number of moves, indicating
that, at this age, each child tries to place the five pegs in a row without paying
attention to the opponent. Rayner (1958b, p. 202) writes that: ‘It seems that
the five year old played a sort of monologue in which he aimed at getting
five in a line but virtually disregarded the other player’s moves.’ By contrast,
the seven year olds were able to anticipate the intentions of the opponent,
and tried to frustrate them.
   Besides the observation of actual games, Rayner submitted eight end-
game problems to the participants and asked them how confident they
were and why they made their choice. The main differences between children
and adults were that adults spent much more time thinking about the next
move, and were able to foresee certain endgames long before the children.
Nevertheless, data from the problem situations indicate that children were
able to think out the relevant strategies.


Tic-tac-toe
A series of studies of tic-tac-toe were undertaken by Sutton-Smith and his
colleagues. Roberts, Hoffmann, and Sutton-Smith (1965) analysed a series of
games played in a tournament by 29 children of the same class, where each
child faced each of his/her 28 classmates; altogether 729 games were recorded
by the children themselves in a booklet. The researchers had access to data
on arithmetic skills measured with a standard test (Test A of the Iowa Test
of Basic Skills) and intelligence (California Test of Mental Maturity). To
measure competence in tic-tac-toe, they used six different scores derived from
the pattern of performance (three winning, two drawing, one not-losing
scores). They also proposed the concept of ‘game velocity’, that is, the rate at
which a game moves to completion (Roberts et al., 1965). Using the scores of
each player to rank order the players, and giving positive signs to the players
of the upper half and negative signs to the others, they produced a ‘com-
petent dispatch rank order’. Results showed that arithmetic ability was
positively correlated with two winning, one drawing, and the not-losing
scores, whereas intelligence was correlated only with one drawing and the
142   Moves in mind
not-losing scores. The winning competent dispatch scores were correlated
with both intelligence and arithmetic.
   Using a ‘tic-tac-toe test’ made of six items representing a game situation,
Sutton-Smith and Roberts (1967) tested the hypothesis that competence in a
particular game would be linked to several psychological (such as cognition,
achievement, aggression) and physical variables. In particular, they were
interested in the relation between game behaviour and type of success
orientation in other forms of behaviour. The results show a shift to more
strategic responses at about the sixth grade. Sutton-Smith (1971) summarizes
the results of another series of studies by pointing out that the better players
are different from those who tend to lose. He argues that it is possible to
distinguish between children who tend to win and children who tend to draw;
while the two groups do not differ in intelligence, they differ in several other
ways. Boys who are ‘winners’ are described as ‘strategists’ by their peers; they
perform better in mathematics, they are more persevering at intellectual
tasks, and quicker at making decisions. In contrast, boys who are ‘drawers’
seem more dependent on adults for approval and more conventional in their
intellectual aspirations. Similar differences are observed in girls; those who
‘are winners are aggressive and tomboyish, whereas girls who are drawers
are withdrawing and ladylike’ (Sutton-Smith, 1971, p. 257). According to the
author, these results support the view that there are functional interrelations
between the skills learned in games and other aspects of player personality
and cognitive style.
   DeVries and Fernie used a Piagetian approach to study the development of
tic-tac-toe strategies in children aged 3 to 9 (DeVries, 1998; DeVries & Fernie,
1990). They videotaped the games of more than 100 subjects, each of them
playing a series of about 10 games against the experimenter; they also inter-
viewed them about their awareness of the other’s intentions and about what
would be ‘good moves’ in several standard situations. Children’s play was
analysed in detail with regard to whether they followed the rules, used block-
ing or two-way strategies, and so on. The authors describe the strategies
observed in several stages: motor and individual play, egocentric play,
cooperation in beginning competition, consolidation of defensive with simple
offensive strategies, and coordination of advanced offensive and defensive
strategies. The same authors also analysed the relationships between
strategies in playing tic-tac-toe and reasoning in a guessing game (Fernie &
DeVries, 1990).
   Crowley and Siegler (1993) were also interested in strategies. They describe
a production system embodying ‘expert’ knowledge of tic-tac-toe, which
involves eight rules (Win, Block, Fork, Block fork, Play centre, Play opposite
corner, Play empty corner, Play empty side). Based on their analysis, they
predicted the order in which rules would be acquired. Three groups of 20
children (6 to 9 years old) and 17 undergraduate students participated in
Experiment 1. They had to solve 32 problems, chosen to allow the assess-
ment of four of the eight rules. Results confirmed that subjects’ strategies
                                      Learning, development, and ageing     143
were rule based, with new rules being added one at a time in the predicted
order. Experiment 2 was designed to explore a phenomenon often observed
in young children (e.g., Rayner, 1958b): they sometimes focus on offensive
goals, and, at other times, on defensive goals, but they rarely pay attention
to both types of goal simultaneously. Forty-five kindergartners played a set
of games against a computer. Results showed that children can adapt their
use of strategy to meet changing circumstances. In Experiment 3, 60 first
graders (7 years old) had to play a set of partially played games against a
computer program. Children achieved flexibility in strategy use by varying
the resources devoted to attaining each goal while pursuing goals in the
order indicated by a fixed-rule hierarchy. Finally, a computer simulation fitted
children’s protocols well.

Nim
Using a methodology inspired by the work of Piaget, Dami (1975) conducted
research on cognitive strategies in four different two-person competitive
games, including a simplified version of nim. In the latter case, participants
were children aged 6 to 16 and young adults. She examined the age differences
in the use of strategies. Results indicated four levels of strategy development.
At the earliest level, 6 to 7 year olds either used a single strategy or behaved
according to unsystematic strategies. At the second level, subjects began to
consider their opponents and attempted to anticipate their moves. At the
third level (9–11 years), subjects seemed more sensitive to the actions of their
opponents. Finally, children at the fourth level were able to discover the
winning strategy and to generalize it to larger numbers.
   More recently, Cauzinille-Marmèche and Pierre (1994) analysed the
learning-by-doing processes used by three groups of ten subjects (8–9 years,
10–11 years, university students) playing two versions of the game of nim.
All subjects played against the experimenter. In the first phase, they played
30 or 40 games with the first, easy version. Then, in the second phase, they
played 30 games with the more difficult version. Results show that, from the
beginning of the first phase, most adults used different types of process:
diversified exploration, hypothesis testing, and deductive generalization.
Initially, only a minority of third graders used these processes. But when
faced with the more complex version, most children made deductive and
inductive generalizations, in at least some of the game states.

Simplified version of chess
Zubel and Rappe du Cher (1980) studied a simplified game, similar to chess,
played on a 5×5 board with five different pieces, each one having arrows
indicating the orientation and number of permitted moves. Their subjects
were 40 children aged 4 to 10. They identified four levels: children around
5 years are mostly centred on their own current move; at age 7, children
144     Moves in mind
can see spatio-temporal connections between their own and their partner’s
pawns; at around 8 years, children consider the multiple consequences of a
move; and from 8 years onwards, children introduce plans and strategies
both for the moves they make on the board, and those they anticipate in their
imagination, including their opponent’s moves.


Hexapawn
Cauzinille-Marmèche and Mathieu (1985) studied a game called hexapawn,
an elementary game played on a 3×3 board. Each player starts with three
pawns, which move like pawns in chess. The goal is to reach the opposite
row first or to block the opponent’s pawns. A game lasts from three to seven
moves. Seventy subjects aged 11 to 16 years participated in the study, playing
several games against a computer. Results indicated that differences in learn-
ing between the various age groups were due more to variations in learning
speed than to variations in learning processes. Results also showed that the
order in which different kinds of error ceased was the same for all subjects.
Problem representations became more complex through the different stages
of learning, and problem analysis became more exhaustive, with deeper
anticipation and more complex goal structures. Five models were built to
account for each of the five stages that were observed during the learning of
the optimal strategy.


Fox and geese
Gottret (1996) studied how 16 Bolivian Aymara boys aged 6 to 16 mastered
the strategies in the game ‘Fox and geese’. He related their performance to
their ability to play the more traditional tic-tac-toe game, as well as to various
cognitive tasks inspired by Piaget. With regard to strategic competence, he
described five levels: (a) absence of cognitive strategies; (b) self-centred activ-
ity; (c) appearance of the first strategies and of consideration of opponents’
strategies; (d) strategies developed in considering opponents’ strategies; and
(e) development of optimal strategies.


More complex games

Chess
Chi (1978) provided a striking demonstration of how knowledge in general
and chunking in particular can interact with developmental differences
in memory tasks. First, Chi replicated the well-known phenomenon that
adults have better memory for digits than children (see Dempster, 1981, for
a review). This result has sometimes been taken as evidence that working
memory capacity increases with age (Case, 1985). Second, Chi compared the
performance of the same participants (six adult novices and six children
                                      Learning, development, and ageing    145
taking part in a chess tournament) in de Groot’s memory task. This time,
children were superior to adults, both when the position was presented only
once and when it was presented several times. Chi interpreted this result as
showing that prior knowledge about a particular domain may compensate
putative developmental differences. Opwis, Gold, Gruber, and Schneider
(1990; see also Schneider, Gruber, Gold, & Opwis 1993) replicated and
extended Chi’s study. They added child novices and adult experts to the
previous design, and also incorporated a control task where a board with a
variety of shapes for the ‘squares’ and the pieces was presented. They also
used random positions in addition to game positions. Children’s average age
was just under 12 years. Adults’ superiority with the digit span task was
confirmed. Both with adults and children, experts’ superiority was greatest
for the meaningful chess positions, reduced but still present with the random
positions, and negligible for the board control task.
   Three and a half years after this study, Gruber, Renkl, and Schneider
(1994) recontacted the children. The first question addressed by Gruber et al.
related to the differences between the players who continued to play chess
seriously (at least one game a week and membership of a chess club) and
those who dropped out, playing chess only casually. When compared to the
players who remained serious, the dropouts (about one-third of the players
who were classified as serious at the first measurement) did not differ in the
digit-span task in the first measurement, but had worse memory in the recall
tasks, both for game and random positions. Gruber et al. consider that this
result supports the hypothesis of selective dropout, perhaps due to differences
in disposition. The second question addressed changes in memory between
the two measurement points. Both serious and casual players improved their
memory for chess-related material. While the progression of the serious
players may be explained by domain-specific knowledge, Gruber et al. suggest
that the improvement of casual players must be explained by general
developmental factors.
   Christiaen and Verhofstadt-Denève (1981) investigated the influence of
chess instruction on cognitive development, school results, and intelligence
test scores. In particular, they were interested in the transition between the
stages of ‘concrete operational thought’ and the next stage, known as the
‘formal-operation’ stage. According to Piaget’s theory, this transition occurs
after around 11 years of age (see Flavell, 1963, for details about stages in
Piaget’s theory). Two groups of 20 fifth graders (average age at the beginning
of the experiment: 10 years 7 months) were tested for cognitive development
using Piagetian tests, school results, and psychometric tests. The experimental
group received chess instruction for one and a half years, during which time
the control group did not receive any specific instruction. The developmental
posttests comprised two standard Piagetian tests (the balance-beam test and
the conservation-of-liquid-quantity test). There was a nonreliable tendency
for the chess group to do better than the control group in the two Piagetian
tasks and in the psychometric tests. Statistically significant effects were found
146     Moves in mind
only for the school results (but see our caveats when we discuss this study
in more detail in Chapter 8). Thus, the study fails to show convincingly that
playing chess affects development in a Piagetian sense.


Awele
A systematic study of awele was undertaken in Ivory Coast by Retschitzki
and his colleagues in the 1980s, using a combination of observations, inter-
views and tests. The first study was aimed at describing the development of
strategies in children (aged 9 to 15) and at investigating possible factors
that might explain the superiority of the better players. To study changes in
the strategies used by these young players and by adults, 73 games were
videorecorded with children and 68 with adults (Retschitzki, N’Guessan
Assandé, & Loesch-Berger, 1986b). The analysis showed quantitative as
well as qualitative changes in playing strategies and behaviour. In particular,
the study focused on the development of behaviour in endgames and in some
typical situations, known as ‘kroos’ (i.e., an accumulation of many seeds that
can be captured in the second round). Retschitzki identified several stages for
each type of situation, showing in detail how the mastery of these tactics
developed. With respect to kroos, four levels were identified: (a) accumulation
without a precise goal (probably by simple mimicry; note that this tactic
can sometimes be efficient); (b) primacy of offensive over defensive aspects
(leading often to heavy losses); (c) beginning of coordination between
offensive and defensive aspects; and (d) efficient coordination of the two
aspects. A similar evolution was described for the endgames.
   Retschitzki conceived a paper-and-pencil task, known as the ‘awele prob-
lems test’, to investigate players’ decision-making processes in choosing a
move. Twenty-eight problems were presented to boys aged 11, 13 and 15 years
(Retschitzki, 1990). A rule-assessment methodology (Siegler, 1976, 1979)
was used to evaluate the results; as there was no ‘good answer’ to each
problem situation, the author compared the pattern of answers given by
each subject to the pattern of answers that different models of reasoning
would have produced. The models differed in several ways, such as the
priority given to attack or defence, the direction of scanning, the depth of
anticipation, etc. Figure 7.1 provides four examples of the models developed
by Retschitzki.
   The analysis showed that players did not answer randomly. Using a
criterion of 70% concordance to evaluate the models proposed, Retschitzki
was able to account for the answers of the majority of the subjects (21 among
28). Simple models were unable to account for the age-related development
apparent in the children’s data. The performance of younger boys was better
explained by models including partial scanning of the situation and a focus
on either defensive or offensive aspects. Contrariwise, older subjects seemed
to behave as if they followed a more global approach, taking into account
both defensive and offensive aspects. However, it was not possible to account
                                       Learning, development, and ageing    147




Figure 7.1 Examples of the models developed by Retschitzki (1990).



for the results of the best player, a 15-year-old boy; the best explanation for
this failure seems to be that none of the models was sophisticated enough to
account for his behaviour.


Checkers
While not strictly about the acquisition of checkers skills, two developmental
studies may be mentioned here. McCloskey (1996) used this game to investi-
gate gender differences in speech styles in first and third graders. She found
that girls were more tutorial in their conversation style with younger partners,
while boys tended to brag or insult their opponent more often than girls.
Mixed-age interaction was also more asymmetric among girls than boys.
During one year, Zan (1996) followed two preschoolers playing checkers
together. Analyses aimed at uncovering the development of interpersonal
understanding showed that impulsive strategies decreased while reciprocal
strategies increased. The two children also improved their ability to resolve
conflicts and produced fewer sessions dominated by conflict.


Development: Conclusions
Research into development has been dominated by Piaget’s framework,
and interesting data have been collected about various aspects of children’s
game-playing behaviour. For people who have observed children playing
school tournaments in various board games, the impression given by this
literature is that an obvious and theoretically important conclusion has been
missed: at an early age, long before the acquisition age of formal abilities,
148   Moves in mind
children can learn to play board games and acquire skills allowing them to
beat (nonexpert) adults consistently. Either they acquire formal skills long
before the age proposed by Piaget, or board-game playing does not require
this level of development. In general, the impression is that the literature
underestimates how far children can go by simply learning a few principles
and memorizing recurring patterns, and overestimates the role of formal
operations. For example, Parker’s (1984) claim that children apply rules
consistently only when they reach the formal operational stage, and that
scoring in card games requires formal operations to calculate probabilities
seems to be refuted by the fact that young children, for instance, 7 year olds,
can play chess, Go, or bridge at a high level, and a fortiori, use their rules
correctly.
   As far as we know, the alternative possibility—that board-game playing
may accelerate the passage to the stage of formal operations—has been tested
in only one study, that of Christiaen and Verhofstadt-Denève (1981). The
pattern of results was in the right direction, but failed to reach statistical
significance. More generally, this study relates to the question as to whether
practice and learning can accelerate development. We believe that board
games offer an ideal domain for tackling this issue, but that their potential
has yet to be fully exploited.
   The Piagetian framework has also been used several times to develop
classification schemas for board games. While adequate at a descriptive
level, these classifications do not seem to have had the success hoped for;
for example, Lancy (1984) failed to reuse Sutton-Smith and Roberts’ (1981)
classification system.
   The progression of playing behaviour has also been studied in several
games. In general, the observations broadly support the stages proposed by
Cleveland (1907) for chess. In particular, the importance of learning to
coordinate attack and defence, as well as other aspects of the game, has
been noted in several studies. In several cases, observations have been sup-
plemented by the construction of formal models (typically, production
systems), which implemented the knowledge acquired at various stages of
development. An important conclusion of these simulations, anticipated by
Cleveland, is that the transition between stages is fluid. Simulation work
about developmental aspects of tic-tac-toe, nim, and awele has been essen-
tially descriptive, but the state of the art has now reached the level where
novel and perhaps counterintuitive predictions can be derived from the
models.
   We have already alerted the reader to the ill-defined boundary between
development and learning. Two studies of ‘development’ have important
consequences for this issue. Chi’s (1978) study and its replication by Schnei-
der et al. (1993) provide evidence that, at least in chess, knowledge is the
overriding factor. The second study is that of Retschitzki (1990), on awele. In
all the variables where reliable differences were found, experience, rather than
age, was the key factor.
                                       Learning, development, and ageing      149
Ageing
The third and last cause for change to be discussed in this chapter is ageing.
Recently, the effect of ageing on expertise has attracted much interest, for the
obvious reason that, in industrialized countries, ageing threatens to erode
the expertise of the working force with potentially serious economic con-
sequences. Although there is much inter-individual variability, the trend is
clearly toward a diminution of abilities such as vision, hearing, memory, and
intelligence (e.g., Schulz & Salthouse, 1999). In the last case, fluid intelligence
(the ability to solve new problems) is more affected than crystallized intelli-
gence (the ability to use knowledge). The hope of current research is that
expertise acts as a moderator on the negative effects of ageing (e.g., Charness
& Campbell, 1988), and that more general compensatory mechanisms may be
identified which counterbalance the loss of cognitive efficacy due to ageing.

Chess
Charness (1981a, 1981b, 1981c) found that younger players recalled chess
positions better than older players of the same skill level. There was an
interaction between skill level and presentation time, the difference between
younger and older players increasing from 1 to 4 seconds. Charness also
found that older players, in spite of lower performance in memory tasks
than younger players of the same skill level, chose equally good moves in a
problem-solving task. Older players were also faster at making decisions.
While clear, these results are difficult to interpret, for methodological reasons:
although the skill level was the same in these experiments, the older players
may have been weaker players than they had been a few years ago; thus, their
(crystallized) knowledge may have been that of stronger players.
   One complication with studies relating age and performance is that there is
an interaction between biological age and ancientness in a domain, an inter-
action that is not well understood. One possible way of tackling this question
is to use computational modelling. Charness (1988) developed a stochastic
model of ageing based on EPAM to explore the hypothesis that older players
slow down and encode less accurate information per unit of time. The model,
which simulates young and old players’ memory for chess positions as a
function of presentation time, implements skill by varying the probability of
detecting salient pieces and finding chunks in LTM. The effect of ageing
is modelled by assuming that older players are slower by a factor of 1.6 at
carrying out these cognitive processes (Cerella, 1985). The simulations show a
good quantitative fit to the human data. The explanation of the interaction
between presentation time and skill is explained as follows: with short times,
the salient piece detector is used rarely, and the main difference comes from
the time necessary to find chunks; with longer times, the salient piece detector
is used more often, which leads to a double superiority for young players.
A limitation of this model is that it cannot predict errors.
150   Moves in mind
   Recently, Mireles and Charness (2002) used a series of neural networks
to explore how knowledge may offset cognitive declines due to ageing. They
simulated the learning of chess opening positions. Ageing was implemented
as modulations in the noise present in the neural network. The simulations
showed that increased knowledge protected performance on a chess memory
span task against the effects of (simulated) ageing. The models could also
replicate the larger variability in the old players’ groups compared to the
young players’ groups.
   A related line of research has attempted to determine the age at which
individuals in various fields achieve their best performance. Overall, the
data do not offer a clear pattern. In professional jobs, there seems to be only a
weak relation between age and performance at work (e.g., McEvoy & Cascio,
1989). By contrast, available data suggest that there exists a relation between
age and creativity. In many domains, maximal performance seems to happen
around 40 years (e.g., artists, musicians, inventors; Schulz & Salthouse, 1999;
Simonton, 1984). This peak occurs earlier in domains such as mathematics
and theoretical physics, and later in domains such as philosophy and history.
In board games, players generally reach mastership in their twenties and
remain competitive well into their fifties. With chess grandmasters, there
is a peak around 35 years, and performance at 20 years is about the same
as at 65 years (Draper, 1963; Elo, 1965; Krogius, 1976; Rubin, 1960). Two
comments should be made here. First, there are several exceptions to this
rule, with players such as Lasker, Kortchnoi, or Smyslov still belonging to
the world elite well after their sixties. Second, there has been a clear trend
towards younger grandmasters in recent years (Howard, 1999, 2001), which
opens the possibility that the peak of best performance has shifted towards
the early thirties.
   Being a chess professional calls for unusual levels of stress, as competitive
games last for several hours, and tournaments for several days. Fine (1967)
suggested that the emotional and physical tension caused by this stress might
have contributed to the early death (between 45 and 55 years old) of three
former world champions (Morphy, Capablanca, and Alekhine). To test this
hypothesis, Barry (1969) compared the longevity of outstanding competitors
with that of minor masters and problem composers. He found that the out-
standing competitors tended to live about a decade less, dying at an average
of 60 years old. There was no difference between those who became world
champions and those who did not, but those who had professional interests
beyond chess tended to live longer. Rubin suggests that these interests may
mitigate the strain due to competitive chess, including that due to the decline
in strength around 40 years. Amateurs should not be deterred by these data,
on the contrary: there is evidence that playing chess and other board games
is associated with a reduced risk of dementia with elderly people (Verghese
et al., 2003).
                                      Learning, development, and ageing    151
Other games
As seen earlier (see also Chapter 9), Masunaga and Horn (2000, 2001) sub-
mitted a large sample of Go players to a dozen of domain-specific and
domain-general tests. They found age-related decline in reasoning, short-term
memory, and cognitive speed, both for Go-specific and general measures.
In Go measures, age-related decline of reasoning seemed to be primarily
mediated by decline in domain-specific memory. Crucially, with the Go-
specific measures of reasoning and short-term memory, decline tended to be
milder with higher skill levels. The results are consistent with the hypothesis
that intensive practice in a domain of expertise mitigates age-related decline
in that domain.
   The absence of ratings in many games makes comparison with chess and
Go difficult. In bao, players typically seem to start playing in their teens
and reach mastery—meaning that they start winning their first games against
recognized masters—in their early twenties. Their peak years are difficult to
determine but do not seem to contradict the data on chess. The famous
players who set records and received national fame had their peak in their late
twenties.
   As in chess, old players fare well in bao, checkers, and international
draughts. In checkers, the world champion matches have long been domi-
nated by men in their sixties and even late seventies—including Tinsley
who was world champion at 68—but this was largely due to the limited player
base. In international draughts players may still peak in their fifties; even in
bao, some 50 year olds have shown exceptional strength.
   Research on African games is subject to a number of biases. Several
authors (especially Béart, 1955) have proposed that the best awele players are
the old illiterate men from the bush. This is a common statement found in
local communities and in publications but it is generally not a statement
made by the expert players themselves. After interviewing five adult players
about eight awele game situations, Retschitzki (1989) found that, contrary to
these statements, the best players are not necessarily old countrymen.
   In order to further test Béart’s hypothesis, Retschitzki (1990) organized a
contest between urban (schooled) and rural (unschooled) players. There were
some organizational problems, because the adults of this particular village
used to play a variant where the rule for capturing seeds was different: instead
of capturing when the number of seeds in the final hole was 2 or 3, they
captured only when this number was 2. This change has an important
influence on the use of tactics, and switching from one set of rules to the
other is not straightforward: the most significant patterns of play have to be
changed. When the usual rules were applied, the young urban players clearly
dominated their rural opponents. But when using the specific rules used in
this village, the contest was more balanced; the best urban player was able
to beat, but barely, the best rural player, an old unschooled farmer. This
means that, while the old men are not necessarily the best players, contrary to
152   Moves in mind
several statements in the literature, they do fare quite well against younger
players.


Ageing: Conclusion
Research on ageing shares with research on development the methodological
difficulty that learning is often a confounding variable. As noted by Charness
(1981a, 1981b, 1981c) and others, the elderly often use compensatory
strategies to offset loss due to age. Other potential confounding variables
come from differences in culture and environment. Attitude towards ageing
changes from one culture to another, with, for example, Western culture often
identifying ageing with lack of independence and certain African cultures
identifying ageing with wisdom (e.g., Béart, 1955; Diop, 1989). Moreover,
a demanding environment, such as that offered by Kortchnoi’s grandmaster
opponents, may elicit more compensatory mechanisms than a gentle
environment such as a local chess club.
   While the number of ageing studies in board games is relatively small to
date, it is likely that important developments will occur in the near future. In
particular, Charness is carrying out a longitudinal study investigating the
ageing process in players of various skill levels. This study, conducted in
the USA, Canada, Russia, and Germany, and using a variety of measures
(verbal protocols in problem-solving situations, eye-movement tracing,
memory tasks, etc.), should clarify several issues that remained unresolved
with cross-sectional designs (see Charness et al., 1996, for preliminary
results).


Conclusion
Reviewing a range of data, mainly provided by the Piagetian and expertise-
research traditions, this chapter has considered the notion of change in
board-game psychology. There is no doubt that this is a difficult question,
and that the research community has only begun to scratch the surface of
the problem. It is symptomatic that the research reviewed in this chapter has
often complemented empirical data with modelling tools, such as production
systems, discrimination networks, and neural networks. These formalisms are
ideal for simulating dynamic systems that change as a function of time.
  We have already offered critical comments at the end of each of the three
sections of this chapter. Here, we will limit ourselves to speculating about
possible directions of research in the future. We have already noted the
presence of several computational models, and one important develop-
ment would be the application of a single model to a variety of board games.
For example, the CHREST/EPAM model could be applied to mancala
games and Go; similarly, a single production system summarizing the stages
of acquisition, such as that developed by Crowley and Siegler (1993) and
Retschitzki (1990), could be used to account for data on a number of board
                                     Learning, development, and ageing   153
games, simple or complex. A second direction of research would be the use
of mathematical modelling to capture change under its various guises. Recent
developments in dynamic systems theory suggest fruitful possibilities
(e.g., van Geert, 1991). Finally, we suggest the use of extended longitudinal
studies, where participants are repeatedly examined in their childhood,
adulthood, and old age. Such a design is obviously difficult, but is not
impossible, as shown for example by research into intelligence and genetics
(Mackintosh, 1998). While the final results of such research would only be
available to succeeding generations, there is no doubt that it would offer
critical information about how the minds of board-game players in particular
and humans in general change over their lifetime.
8      Education and training




Introduction
In the previous chapter, we explored how skill develops. In this chapter, we
will address two related questions. First, does learning to play a board game
yield skills that transfer to other domains? Second, can we develop methods
to optimize the acquisition of board-game skills, from beginner level to
master level?
   Articles and books that promote the use of play or games in education
are common. It is also relatively easy to find empirical research on play,
with most papers being devoted to symbolic play, fantasy play, and socio-
dramatic play in relation to preschool children. Researchers (e.g., Christie,
1991; Moyles, 1989) have tried to show that play can be productive for a
number of purposes: emotional development, social development, cognitive
development, creativity, language, and early literacy development.
   Some researchers suggest that games, just like play, can be used to teach
both general and specific knowledge. Teachers may use games in the class-
room because they believe that these activities contribute to children’s general
development or to their learning of mathematics, language, or history.
Among the means that adults could use to foster mathematical development
during play, Jarrell (1998) highlights how one could initiate school mathe-
matics using games such as Connect Four, checkers and chess. A strategy for
teachers would be ‘to encourage the playing of games that have a rich array
of mathematical problems embedded in them’ (Jarrell, 1998, p. 65). Games
from other regions could also help the acquisition of knowledge about other
countries or cultures.
   Board games are taught in several countries. For example, chess is taught
in American, French, and Argentinian schools, either as an elective or com-
pulsory topic. Draughts is played in elementary or secondary schools in
Russia and the Netherlands. Awele is taught in some American and European
schools, while Go is taught in both Western and Japanese schools.
   In the board-game community, as in the educational community,
statements abound about the presumed efficacy of using board games for
fostering education. It is perhaps chess that has generated the most optimistic
156   Moves in mind
claims. Some have argued that chessplaying makes children smarter or that it
increases mathematical abilities. Others have suggested that chess lessons may
motivate underprivileged students, such as black youngsters in inner cities.
(A variety of these positions can be found on the education site of the USCF:
http://www.uschess.org/scholastic/sc-research.html.) In spite of these claims,
there is surprisingly little empirical evidence on the educational benefits of
games. This lack of evidence is especially true for board games as opposed to
the use of simulation and video games.
   Before reviewing the empirical evidence that skills acquired when playing a
board game transfer to other domains, we address the question of ‘transfer’.
We then discuss the available empirical evidence, first for chess, and then for
other board games. We conclude that, despite the strong assertions often
found in the educational and board-game literature, the evidence in favour of
using board games is both sparse and inconclusive.


Board-game instruction and the transfer of skill

The question of transfer
The question of transfer has occupied researchers in psychology and in
education for more than a century, and the conclusion is that it is unlikely
that a set of skills acquired in a specific domain will generalize to other
domains, unless there is an overlap between the components of both skills
(Anderson, 1990a; Singley & Anderson, 1989; Thorndike & Woodworth,
1901; Travers, 1978). For example, abilities acquired learning geometry are
likely to help in the study of more advanced mathematics, such as calculus,
but would not facilitate the study of history. Similarly, it is doubtful that
practice in a domain, however intensive, would lead to better cognitive
general abilities. (Incidentally, a consequence of this view is that teaching
Latin or geometry as a way to ‘muscle the mind’ has no empirical support.)
The best bet for obtaining transferable skills seems to be to teach just that:
transferable skills. That is, generic skills and strategies that help improve
learning, problem solving, or reasoning. There is some empirical evidence
that teaching such skills leads to abilities that can be applied in several
different domains (Grotzer & Perkins, 2000).
   As is apparent in most chapters of this book, and as is strongly argued by
Ericsson and Charness (1994), research into expertise suggests that transfer
becomes less likely as one moves up the expertise ladder in a domain; this
is because the skills acquired become increasingly specific. In addition, it
has been well established that becoming a world expert in domains such as
games, mathematics, music or sports, requires an almost obsessive dedication
to the domain, including huge amounts of practice (Bloom, 1985; Chase &
Simon, 1973b; de Groot, 1946; Ericsson et al., 1993). As time is a limited
resource, it is inevitable that this investment in a specific domain will impair
the acquisition of other skills. Conversely, the hypothesis that domains such
                                                  Education and training    157
as mathematics provide skills for board games is equally problematic (see
our discussion of intelligence in Chapter 9).


Empirical evidence from chess
Recently, in 2001, the potential advantages of chess for education were
discussed at the ‘George Koltanowski Memorial Conference on Chess and
Education’ in Dallas, Texas, and in an ensuing book summarizing the
main contributions (Redman, in press). One chapter of this book (Gobet &
Campitelli, in press) reports the outcome of a detailed evaluation of the
available studies exploring possible transferable skills from chess instruction.
Using a variety of bibliographic and database sources, Gobet and Campitelli
combed the literature in search of studies meeting three criteria: (a) presence
of an empirical investigation; (b) objective measure of the potential effect(s);
and (c) presence of enough detail to evaluate the methodology used and the
results obtained. They could find only a handful of studies—essentially those
that we will review below. Disappointingly, while some chess experiments
have been well publicized, such as that carried out in the late 1970s in
Switzerland (Dextreit & Engel, 1981) and that conducted in the early 1980s
in Venezuela (Ferguson, undated a), no detailed report was ever published to
assess their outcome.
   The available studies were submitted to a rather stringent evaluation:
the design of each experiment was compared with what can be called the
‘ideal experiment’ (e.g., Keppel, 1982; Travers, 1978). In this experiment,
participants are randomly allocated to a treatment group and to two control
groups (one placebo group and one no-treatment group); measurements are
taken before (pretest) and after (posttest) the experimental manipulation; and
both participants and experimenters are blind to the fact that they belong to
an experiment, and, a fortiori, to the goal of the experiment. Following Gobet
and Campitelli’s (in press) report, we first review the main empirical studies,
roughly in chronological order, and then evaluate the possibility of transfer
from chess instruction to other skills.


The Zairian study
In a study conducted in Zaire, Frank and d’Hondt (1979; see also Frank,
1981) tested two hypotheses. The first was that learning chess depends on
a number of cognitive aptitudes, such as spatial ability, perceptual ability,
reasoning, creativity, and general intelligence. The second was that the causal
link also goes in the opposite direction: learning chess affects the develop-
ment of these aptitudes. Ninety-two teenagers (from 16 to 18 years old) were
randomly assigned to either a compulsory chess group or a control group.
The chess group met twice a week for one hour, throughout one year. Instruc-
tion consisted of lectures, practice, games against the teacher, and tests. The
control group did not carry out any specific activity.
158   Moves in mind
   Before and after the intervention, participants received two psychometric
tests (the Primary Mental Abilities Test, and the General Aptitude Tests
Battery), with a total of 12 subtests. Three other tests, with a total of six
subtests, were given only at the beginning of the study: the Differential
Aptitude Test, the D2 test (a test of attention), and the Rorschach test (a pro-
jective test using inkblots). Finally, chess quizzes were used to estimate
chess skill at the end of the year with the experimental group. (The reader is
referred to texts such as Cronbach (1960) or Sternberg (2000) for detailed
information about the tests mentioned in this chapter.)
   Frank and d’Hondt’s first hypothesis—that some cognitive abilities predict
chess skill—was supported. While no reliable correlation was found with
the variables extracted from the Rorschach test, some of the psychometric
measures in the pretest correlated with chess skill after one year of instruc-
tion (‘spatial aptitude’ and ‘numeric ability’ from the Primary Mental Abil-
ities Test; ‘administrative sense’ and ‘numeric aptitude’ from the General
Aptitude Tests Battery; and ‘office work’ from the Differential Aptitude
Test). There was also some support for the second hypothesis—chess instruc-
tion fosters skills that can generalize to other domains. A comparison of the
scores on the posttest showed that the chess group was better than the control
group for ‘numerical aptitude’ and ‘verbal ability’. Nevertheless, Gobet and
Campitelli (in press) argue that the results for ‘numerical aptitude’ are not
convincing, because the difference between the experimental and control
groups is better explained by the fact that the control group, for unknown
reasons, performed badly in the posttest than by the fact that the experi-
mental group improved its performance. This result weakens the impact of
the study because, as noted above, the aim of this part of the experiment was
to show that chess instruction improves abilities in other domains.
   Frank and d’Hondt mention two cautionary remarks that are of interest
for chess instruction: first, most students lacked motivation and interest,
and, second, students obtained low test results overall. Teachers planning
to organize compulsory chess classes may want to reflect on the lack of
motivation found in this study. A further source of reservation is that most
of the tests used in the study were not developed for an African culture and
therefore may have been invalid (e.g., Cronbach, 1960), although, as noted by
Frank and d’Hondt, it is unclear how this would have affected the outcome
of their study, as all participants received the same material.


The Belgian study
As seen in Chapter 7, Christiaen and Verhofstadt-Denève (1981; see also
Christiaen, 1976) were interested in how chess instruction affects children’s
cognitive development, and, in particular how it may speed up the
appearance of the stages proposed by Piaget’s theory. Forty Belgian fifth-
grade boys (with an average age of 10 years 7 months at the outset of the
experiment) were randomly assigned either to a chess group or to a control
                                                   Education and training     159
group. The chess group received compulsory chess instruction for one
hour weekly, on Fridays after school, while the control did not carry out any
specific activity and went home; this regimen lasted for 42 weeks, spread
over one and a half years during school term. Chess instruction consisted
of theory, practice games, and tournament games. In order not to raise
children’s suspicion that they were taking part in an experiment, no pretest
was given. The posttest comprised two standard Piagetian tests (the balance-
beam test, and the conservation of liquid test). The study also used as
dependent variables school results at the end of the year, as well as a series
of aptitude tests given annually to the sixth-grade children for orientation
purposes. For the treatment group, chess skill was estimated by a seven-round
tournament.
   Although the chess group tended to do better than the control group, no
reliable differences were found in any of the posttests. There were clear-cut
differences for the school scores, both after 5 months of chess instruction,
and at the end of the experiment. Even so, Christiaen (1976, p. 61) remains
cautious, noting that the teachers ‘were aware of the trial and thus con-
sciously or subconsciously could act favourably or unfavourably in their
relation with the pupils’, which may possibly have confounded the results.


The Texas study
Liptrap (1998) investigated whether participation in a chess club affects
elementary school students’ standardized test scores. The study comprised
571 children, in a school near Houston, Texas, and compared their third-
and fifth-grade scores on the Texas Learning Index (TLI) of the Texas
Assessment of Academic Skills. A strength of the TLI is that it allows one to
compare students across years and across grades. Students who participated
in a school chess club in fourth and/or fifth grade were compared to students
who did not. The chess group consisted of 67 students (74.6% male),
and the nonchess sample 504 students (50.8% male). Students were further
partitioned into special-education students, regular students, academically
able students, and gifted and talented students. The chess group and
the control group consisted mostly of regular students (34.3% and 53.4%,
respectively).
   At the third grade, before the start of chess instruction, there was a (statis-
tically nonsignificant) tendency for the chess group to obtain better reading
and mathematics scores. By the fifth grade, the chess group outperformed the
control group in both domains, a difference that was most apparent with
the regular students. While both groups improved these two scores over the
two years of the experiment, the progress was more marked for the chess-
players (about twice the improvement of the nonchessplayers in both reading
and mathematics); no information is given about the statistical reliability of
this difference.
160   Moves in mind
The Pennsylvania studies
Ferguson (undated a, undated b) reports three studies that are often cited in
the chess literature as support for chess instruction. As will be exemplified by
the description of the following study, and as is discussed in detail by Gobet
and Campitelli (in press), there are various weaknesses in this line of
research. Ferguson’s (undated a) study provided experiences that could help
develop critical and creative thinking. The participants, who were gifted
students (with an IQ equal or higher than 130) in grades 7 to 9, could choose
between chess, dungeons and dragons, Olympics of mind, problem solving
with computers, creative writing, and independent study. Each group met
once a week for 32 weeks. Participants were tested in the Watson-Glaser
Critical Thinking Appraisal Test (CTA) and in the Torrance test of creative
thinking, both at the beginning and at the end of the year. The chess
group significantly outperformed the other groups in the CTA test. With the
Torrance test of creative thinking, the chess group showed statistically
significant improvement in ‘fluency’, ‘flexibility’, and ‘originality’ when it was
compared to the population norms and the nonchess group. There was
also a significant difference in ‘fluency’ and ‘originality’ for the chess group
compared to the computer group. These results must be treated with caution,
for several reasons: the students switched activities either quarterly or semi-
annually, the sample was taken from a gifted population, and the sample was
rather small (15 students in the school chess club).


The Bronx study
Margulies (undated) tackled the question of whether chess instruction
improves reading scores. The study took place in the South Bronx, New York
City, where it is notably difficult to keep children interested in school activi-
ties. In the first year, mid-elementary schoolchildren who had voluntarily
joined a chess club received instruction by chess masters; this instruction was
enhanced by computer-supported chess activities in the second year. For the
pretest and posttest, Margulies used the scores on the ‘Degree of Reading
Power Test’, which all subjects had taken both before chess instruction and
after, as part of standard school evaluation. These scores were compared to
the national norm for the same grade and to the scores of the average student
in the school district.
   The chessplayers showed more improvement than the country and school
district averages, which both showed no gain. This result is not affected by
the possible confound that the chess group had higher entry-level scores:
compared with a non-chess control with similar entry-level reading
scores, the chess group still showed more gain. However, the use of a quasi-
experimental design and the lack of a control group make conclusions
about the effect of the treatment highly tentative, which is acknowledged
by Margulies. In particular, the risk of self-selection looms large. In addition,
                                                  Education and training    161
the effect of playing chess was confounded by the use of computers in the
second year.


The Brooklyn study
In a well-controlled experiment, Fried and Ginsburg (undated) investigated
whether chess instruction affects the development of perceptual and visuo-
spatial ability, as well as attitude toward school. Thirty fourth and fifth
graders (15 males and 15 females), with mild learning and behavioural
problems, were randomly assigned to three groups: chess, counselling (which
was used as a placebo group), and no contact. Chess instruction consisted
of lectures, demonstrations, and games. After 18 weeks, three tests were
given: the figure completion subtest of the revised version of the Wechsler
Intelligence Scale for Children, measuring visual awareness to detail; the
block design subtest of the same test, measuring visuo-spatial ability; and a
survey of school attitudes. No difference was found between the three groups.
Additional analysis showed the presence of an interaction between gender
and treatment in the block design task and the school attitude test; the
pattern of these two interactions was unsystematic and unexpected by Fried
and Ginsburg.


Overall evaluation
For a number of practical, administrative, and ethical reasons, it is difficult
to use the ideal design we have described at the beginning of this chapter. In
fact, most research in education has chosen weaker designs, such as employ-
ing groups already formed (e.g., children attending a club vs. children not
attending). The experiments we have reviewed are thus typical of educational
research. But the fact that these weaker designs do not assign participants
randomly to groups imposes serious limitations on the conclusions that can
be drawn about direction of causality (e.g., Travers, 1978). For example,
several studies found that the chess group did better than the control group
on a certain measure. Is this difference due to chess instruction, or rather to
some kind of self-selection, for example the increased tendency for intelligent
children to play chess? Or, perhaps, a third variable is involved. Gobet and
Campitelli (in press) give the example of the ability to cope with time
pressure, which would positively affect both chessplay, where thinking time
is limited by a clock, and performance in intelligence tests, where some of
the subtests have to be carried out either under time restrictions or with time
bonuses.
   Thus, while most of the studies reviewed in this chapter obtained some
positive effect, this outcome is mitigated by the fact that they all suffered from
methodological weaknesses. As noted by Gobet and Campitelli, only three
studies (Christiaen & Verhofstadt-Denève, 1981; Frank & d’Hondt, 1979;
and Fried & Ginsburg, undated) randomly assigned participants to treatment
162   Moves in mind
and control groups. In these studies, the results only weakly supported the
hypothesis of transfer from chess instruction. The other studies used designs
that are too weak to infer the causal relation between the variables of interest,
and often did not have any protection against the placebo effect or possible
nonintentional influences from the teacher or the tester. Another weakness
is that, in some studies, a large number of measures were collected, with the
consequence that some of the statistical tests may have turned out to be
significant just by chance. (None of the reviewed studies included statistical
corrections for multiple tests.) Finally, no study investigated whether chess
instruction has long-term benefits, or controlled for the characteristics of the
teacher (who often was a motivated chessplayer convinced of the virtues of
chess instruction), or replicated previous work.
   In sum, there is little empirical evidence from chess research that contra-
dicts the ‘official’ conclusion that cognitive skills do not transfer much from
one domain to another. According to Gobet and Campitelli, the extant
evidence indicates that (a) the effects of optional chess instruction are still
open to question; (b) compulsory instruction may not be recommended, as
it seems to lead to motivational problems; and (c) while chess instruction
may be beneficial at the beginning, the benefits seem to decrease as chess skill
improves, because of the amount of practice necessary and the specificity
of the knowledge that is acquired. In general, the results are in line with
de Groot’s (1977) assessment that, while chess instruction may provide
‘low-level gains’, such as improvement in concentration, learning to lose,
and interest for school in underprivileged environments, it is less likely to
provide ‘high-level gains’, such as increase in intelligence, creativity, and
school performance.


Other board games
As with chess, there is no shortage of claims that other board games have
educational benefits. Unfortunately, we were able to find only one controlled
experiment testing these claims. Therefore, in this section, we will mainly limit
ourselves to a description of the potential benefits of various board games,
starting with elementary games.
   Tiss (1997) reviews a number of ‘family board games’, such as ‘Don’t Spill
the Beans’, ‘Bingo’, and ‘The Memory Game’. She identifies several benefits
of playing them with children, such as the opportunity to apply and
strengthen the mathematical skills learned in school, and the possibility
to develop abilities such as memory, concentration, and attention. Tiss
emphasizes that these games have the advantage that children become
actively engaged, and interact with other learners—activities that are seen
as being beneficial for learning. Unfortunately, no empirical evidence is
presented in support of these assertions.
   In her book about numbers in Africa, Zaslavsky (1973, p.130) speculates
about the potential educational value of mancala. Accessible in its simplest
                                                 Education and training   163
form to young children, mancala can encourage the child to count. Accord-
ing to Zaslavsky, the child ‘learns the concept of a one-to-one correspondence
as he drops each of his counters into each of a sequence of consecutive holes.
Soon he learns simple sums . . . A move of eleven means he will drop his last
bean in the hole just preceding his starting position, the kind of addition
useful in reading the clock.’ Zaslavsky also mentions that the variant called
omweso ‘which permits reverse moves, introduces the concept of negative
numbers. As they work with the sixteen holes in their own territory, players
see that a backward move of six spaces is the equivalent of a forward move
of ten and that a move of (−3) brings them to the same position as a move of
(+13).’ Deledicq and Popova (1977) similarly advocate the use of awele in
teaching mathematics at a higher level. They show, for example, how one can
teach combinatorial concepts through the analysis of the game. In particular,
they create a variant that they call ‘micro-awele’ in order to show how to
analyse all the possible moves.
   De la Cruz, Cage, and Lian (2000) used two mancala games, Kalaha (a
commercial invention) and Sungka (as it is played in the Philippines), to
teach mathematics and social skills to students with disabilities. They found
that these games facilitated the learning of counting, estimation, and basic
operations of addition and subtraction; given that players distribute counters
around the board, these games may also contribute to the improvement of
fine-motor skills; and, since the games are played in different cultures, they
may encourage multiculturalism. In general, it is believed that children with
learning difficulties benefit from hands-on and activity-based instruction;
alternative approaches, including playing mancala games, may also turn out
to be beneficial (Wohl, Deering, & Bratina, 2002).
   The only experimental study we found is that reported by Tano (1985,
1989) who carried out research in the Ivory Coast to demonstrate the benefits
of playing awele; the research was explicitly based on the ‘prototypical play’
training paradigm also called ‘play tutoring’ (Smilansky, 1968), in which
adults deliberately encourage children to play. Sixty-four fourth graders from
two different areas of Abidjan were assigned to an experimental and a con-
trol group. The experimental group was taught awele; the control group
received an ‘affective support’ treatment. Before and after the intervention,
participants filled in two psychometric tests (measuring verbal intelligence
and nonverbal intelligence) created by Ivorian psychologists and validated for
the Ivorian population. The analysis showed a significant positive effect of
the training with awele. Unfortunately, no precise description of the training
procedure or of the psychometric tests is provided.


Teaching the rules and basic instruction
There exists substantial literature, now supplemented by computer software,
introducing beginners to games played in industrialized countries. Typically,
instruction books are written and methods are developed by players rather
164   Moves in mind
than by educationalists (see Dextreit & Engel, 1981, for a discussion of chess
education). We must be aware that teaching methods may be different in
nonindustrialized countries. For example, few books have been written about
African games such as awele or bao. The level of explanation remains basic
and the audience consists mostly of beginners at the game. (Not revealing
intricate strategies in writing still gives expert players a competitive edge.)
   Dollekamp (1985, pp. 165–6) argues that the application of educational
principles on the teaching of draughts should separate the purpose of
becoming better at the game and the purpose of teaching the game to
children or people unfamiliar with its rules and strategies. His concept for
teaching draughts in schools was developed for this latter purpose and was
later successfully implemented by Buist (unpublished) in primary school
education.
   In the game of Go, teachers often recommend ‘soufu’, which is a traditional
Japanese learning method consisting in reconstructing a game based on a
given position, with the student playing both sides. Used as a technique to
acquire explicit knowledge, it helps the student focus on relevant features—
a nontrivial accomplishment in Go, whose complexity often confuses
beginners. Burmeister (2000) was interested in whether a slight modification
of soufu could also lead to the implicit acquisition of knowledge (Reber,
1967). Can players pick up the underlying regularities of the sequences of
moves rather than simply learn them by rote? The treatment, which lasted for
five sessions given on different days, consisted of the penny-guessing and the
sequential move-prediction task we have described in Chapter 5. To simplify
the task, a 9×9 board with 10 stones was used. Performance of two beginners
was evaluated at the beginning and the end of the experiment with a pretest
and posttest that involved predicting the moves of an unknown game.
Informal analysis of the results indicated that both participants showed
improvement, which supports the hypothesis that there was some implicit
learning of sequences of moves. Unfortunately, the generality of this result is
limited by the fact that there was no control group.
   Since learning mancala games from a piece of paper is notoriously
difficult, both in Africa and in the Western world, learning by doing, being
told, and observing is intrinsic to the teaching system, and is more important
than in games like chess or checkers. A player who is able to apply the bao
rules flawlessly already has a degree of skill. It is important to note that a bao
teacher will frequently show and explain moves by reversing and replaying
them. This technique of reversing moves has also been used in some cognitive
experiments (see Chapter 5), and is considered a separate skill which only has
value as a teaching tool.
   There is almost no research comparing instruction methods at the
beginner’s level. The only exception is a study conducted in Switzerland by
N’Guessan Assandé (1992) in order to describe the learning mechanisms
in awele. He compared one group of nine psychology students and one group
of nine chessplayers; none of the participants knew how to play awele before
                                                  Education and training    165
the experiment. After being taught the rules, the participants were assigned
to one of three learning conditions: (a) practice without any help during 10
hours; (b) observation of an expert player (5 hours), then practice (5 hours);
and (c) a demonstration and an explanation of the key concepts (5 hours),
then practice (5 hours). The participants or the expert played all their games
against a computer program. N’Guessan Assandé found that chessplayers
learned faster than students and that the condition enabling the steepest
progress was the demonstration with explanation of concepts. Unfortunately,
the experimental design did not allow one to separate the effects of explan-
ation from the effects of demonstration per se. We should also emphasize
that the study focused only on the early steps in learning; the program did not
play well and even the best players did not reach a high level. The results also
show that the strength of the players (measured by their Elo ranking for
the chessplayers or their knowledge of other strategy games for the students)
correlated positively with their acquisition of awele strategies.


Training and coaching at an advanced level
So far, we have dealt with the questions of whether learning a board game
impacts on general cognitive and non-cognitive skills, and of how the basic
rules of the games are taught. Another aspect of board-game education is
whether good teaching and coaching techniques have been developed to
foster the development of high performance in a given game. This question
is actually of interest for psychologists and educationalists beyond the realm
of games, because efficient techniques may also be applicable in teaching
standard school subjects such as mathematics or science. Unfortunately,
there have been few controlled experiments addressing this topic. We first
present some informal approaches to training, mainly developed by players
themselves, and then discuss a few attempts to apply current knowledge
in psychology and education to teaching a specific board game. Finally,
we address the question of the media used in board-game teaching, and in
particular, whether coaches are necessary.


Informal approaches
While not comparable to the massive literature on the technical aspects of
the game, there is a large body of non-scientific literature in chess about
training methods, and such a literature exists for other board games as well,
notably Go, checkers and draughts, Chinese chess (shiang qi), and shogi. In
general, there is broad agreement about what students should do to become
masters, and most of these recommendations are actually in line with current
scientific knowledge about human learning and memory. The emphasis is
on the amount of work necessary for acquiring the explicit and implicit
knowledge that characterizes masters—what de Groot (1946) calls their
‘system of playing methods’. The advice given includes ways to find a balance
166   Moves in mind
between rote learning and the understanding of general principles, and
methods for practising various aspects of the game. In line with this advice,
board-game players spend much time analysing games (their own and those
of masters), as well as practising tactical and strategic skills with quizzes in
books or journals.


Formal approaches
While some publications on chess training mention scientific research in
psychology (e.g., Bönsch, 1987; Kotov, 1971; Krogius, 1976), few base their
recommendations directly on scientific theories. At least two chess books
(Fischer, Margulies, & Mosenfelder, 1966; Lasker, 1997) used a technique
called ‘programmed learning’, which Skinner (1954) developed from his
theory of operant conditioning. Munzert (1988) applies various techniques
from sport psychology to chess, and summarizes practical recommendations
from (informal) Soviet chess psychology. In general, the success of a method
is more important to the teacher than its possible academic support. For
instance, Krajenbrink (1995) made a comparison of 10 teaching methods for
the game of draughts used by known draughts trainers in various countries.
His evaluation was based on the success and inventiveness of the trainers and
their methods rather than the academic support for the theory in use.
   Gobet and Jansen (in press) apply the template theory (see Chapter 3) to
chess training. As this approach builds directly on one of the theories of
expertise discussed at length in this book, we will develop some of its ideas
in further detail. Based on what they consider chess research’s key findings—
limited STM, perceptual chunks, domain-specific memory, multilevel
encoding of knowledge, slow acquisition of new information, and selective
search—Gobet and Jansen derive three educational principles from the
template theory. First, the acquisition of knowledge best moves from simple
to complex; second, learning is optimized when the elements to be learnt are
clearly identified; and third, learning is facilitated by following an ‘improving
spiral’, where learners start from simple aspects of specific material (e.g.,
an opening variation), and then keep on coming back to it by progressively
enriching their knowledge base with new information. As is known from
memory research, the creation of multiple cues strengthens memory traces
(e.g., Baddeley, 1990) and therefore the likelihood that they will be retrieved
usefully in the future. These principles are in line with some leading theories
in education (e.g., Anderson, Corbett, Koedinger, & Pelletier, 1995; Travers,
1978), but also directly conflict with others, such as the situated-learning
approach (Lave & Wenger, 1990) and the problem-based approach (Boud &
Felleti, 1991). Gobet and Jansen illustrate the idea of an improving spiral
by the ‘decomposition method’. With this technique, one starts by selecting a
typical position from a given opening. Then, one removes all pieces but Kings
and Pawns from the position, and studies and plays the endgames that may
occur from this position. Gradually, one adds pieces of various sorts to this
                                                  Education and training    167
skeleton position, or various aspects of the Pawn structure, still playing and
analysing variations that could arise from these positions.
   While most of the advice given in the literature is consistent with the
template theory used by Gobet and Jansen to inform training practices,
there are some instances where the theory makes recommendations which
clash with often proposed advice. In these cases, common-sense views about
teaching are questioned by principles derived from fundamental research.
For example, Wetzell (1997) and others recommend training short-term
memory and imaging skills in order to improve search and problem-solving
capabilities. Gobet and Jansen criticize this advice, referring to the available
data showing that STM capacity and general visuo-spatial abilities do
not correlate with skill (see Chapters 5 and 9). Several authors, notably
Kotov (1971, 1983), suggest that practising the ability to look far ahead is an
effective way to improve skill. Gobet and Jansen take issue with this recom-
mendation, noting that problem-solving abilities in general and depth of
search in particular are side effects of a well constructed knowledge base
(e.g., Gobet, 1997a) and that the understanding of a position through pattern
recognition actually cuts down the need for looking ahead (de Groot,
1946). Another recommendation of Kotov—to visit each branch of the
search tree only once—is also criticized. It is argued that revisiting the same
branch several times is made necessary by limits of human cognition, mainly
information decay in STM and in the mind’s eye. Moreover, as noted by de
Groot and Gobet (1996), reinvestigating the same line repeatedly allows one
to propagate information from various nodes in the search tree.
   As a final example, we may consider the advice of playing blindfold for
improving chess skill in general. Gobet and Jansen suggest that this is useless,
and perhaps even detrimental to one’s development. This is consistent with
existing nonacademic views on blindfold play, which state that blindfold
play could even lead to insanity (e.g., Dextreit & Engel, 1981; Hearst,
1967). In particular, in Russia, trainers have been known to forbid blindfold
simultaneous games for that reason. On a less dramatic note, Gobet and
Jansen mention empirical data showing that the ability to play blindfold
comes as a consequence of having acquired a well-organized and easily
accessible knowledge base (Ericsson & Staszewski, 1989; Saariluoma, 1995;
see also Chapter 4), and not the other way around. Although Gobet and
Jansen provide a teaching method based on existing scientific theory, there is
as yet no experimental evidence that confirms the validity of this approach.
Whether these recommendations are beneficial in practice is a question to be
settled empirically, by comparing them with other methods of instruction.


Media of instruction: Coaches, textbooks, and computer programs
According to the chunking/template theory, the order of presentation and
the type of segmentation of the material are critical for the training out-
come. In order to use students’ time optimally, it seems advisable to have
168   Moves in mind
the instruction material segmented in optimal chunks by a coach, a book, or
computer software.
   According to Gobet and Jansen (in press), there are two aspects to
coaches’ contributions. First, their technical contribution includes selection
and preparation of study material, identification and remediation of trainee’s
weaknesses, feedback on performance, and advice about how to play against
the trainee’s opponents, including preparation of specific variations. Second,
their personal contribution includes management of the trainee’s motivation,
and optimization of study time (e.g., by reducing the time spent in adminis-
trative chores). The necessity of having a coach has sometimes been debated;
for example, Charness et al. (1996) found no correlation between chess skill
and the presence of a coach, while such a correlation was found by Campitelli
and Gobet (2003). Research in education has shown that students take more
advantage of a private tutor than of a shared classroom tutor (Bloom, 1984).
This advantage, if it applies to board games as well, would support the use of
a private coach.
   In industrialized countries, books have been the main vehicles for trans-
mitting board-game knowledge. Gobet and Jansen (in press) argue that
books often violate sound psychological and pedagogical principles. For
example, most books present schemata and methods specific to a small range
of positions, which may not match the positions students will meet in their
own practice.
   Current computers offer an invaluable aid for creating and using game
databases, and for practising with an opponent. In particular, playing with a
strong computer program is likely to improve one’s tactical skills, and can
be instrumental in practising typical positions and testing new ideas. In
games where teaching the rules already constitutes a problem, computer pro-
grams have been helpful in internationalizing the games. While teaching
strategy and tactics is thought to be more efficient and effective, extensive
practice against computers may bridge part of the gap between novice and
expert in games where instruction is hard to find. More research is needed to
demonstrate such effects.


Conclusion
This chapter illustrates the paradox at the heart of the literature on board
games and education. Although it addresses questions of practical impor-
tance, and although strong claims have been made about the presumed
benefits of playing board games, little experimental research has been carried
out, and the available data are not conclusive. As noted in our discussion
about transfer, current evidence does not stand up to critical analysis using
strict criteria of evaluation. The data appear to support using board games in
education, but more rigorous research needs to be done before one can be
confident that board games have positive effects on instruction in general. It
is our hope that a review of the literature 10 years from now will have more
                                                 Education and training    169
empirical data to report, and will rely less on verbal arguments about the
potential value of board games for instruction.
   The picture is similar with respect to educational techniques aimed at
teaching the basics of board games, and those aimed at allowing progression
to higher levels: in spite of extensive technical literature, little empirical
evidence is available about the merits of the proposed methods. Perhaps the
presence of computer instruction and playing engines will make it possible,
in the future, to collect data automatically from learners in order to test and
improve current methods.
9      Individual differences and the
       neuropsychology of talent




The topic of individual differences has been left implicit in the previous
chapters. If mental capabilities vary within a population, there is no doubt
that this could have consequences on performance in perception, learning,
memory, and problem-solving tasks. In particular, differences in learning
may affect the choice of educational regimens. Historically, individual dif-
ferences and their effect on cognition have been studied under the umbrella of
the psychology of intelligence. In recent years, in part due to progress in
neuroscience, there has been a resurgence of interest in the links between
intelligence, talent, and the biological bases of cognition.
   It is common to contrast the ‘talent tradition’, which goes back to Galton
(1869) and emphasizes the role of nature, and the ‘expertise paradigm’,
centred around Chase, Ericsson, and Simon, which underscores the role
of practice. This contrast does justice to the followers of Galton, who con-
sider the role of the environment of little significance, and the followers of
Ericsson, who have taken the strong position that inherited individual
differences—except for differences in motivation—do not affect the develop-
ment of expertise (Ericsson & Charness, 1994; Ericsson et al., 1993). How-
ever, it should be pointed out that Chase and Simon (1973b) themselves,
while emphasizing the role of practice, were also open to the possibility of
genetically determined individual differences. As is often the case in such
highly polarized debates, the review of the empirical evidence only provides a
split verdict, with support for both positions. Regrettably, there has been little
research on the nature of individual differences in board games, on emotions
and motivation, or on personality traits. Nonetheless, the few studies we were
able to uncover clearly demonstrate the role of motivation and emotions in
problem solving.
   If the talent approach is correct, one should be able to uncover biological
mechanisms (genetic or not) underlying the extraordinary performances
of board-game grandmasters. The theory developed by Geschwind and
Galaburda (1985) provides such mechanisms and aims to account for a
number of phenomena, including the development of talent in visuo-spatial
domains. Although the evidence does not always support its predictions,
this theory enables the integration of the available data into a consistent
172   Moves in mind
framework. Some of the research we will review, in particular that based on
brain-imaging techniques, has been carried out only in the last decade. It is
therefore likely that our understanding of the biological underpinnings of
talent and expertise is still rudimentary.


Intelligence and visuo-spatial abilities
Recently, research into board games has come under the spotlight of popular
science (Brown, 2002), following Howard’s (1999, 2001) attempt to use
chess and Go to support the hypothesis that average human intelligence
is rising. Howard argued that the increasing number of young players
among the world’s elite provides evidence for this rise. While intriguing,
this proposal has several weaknesses, including the fact that the increased
participation of young players in top-level chess can be explained by other
mechanisms, such as better coaching methods, apparition of computer data-
bases and playing programs, and increase in the number of tournaments and
monetary incentives (Gobet, Campitelli, & Waters, 2002). The weakest link
in Howard’s argument is perhaps that the relation between board-game skill
and intelligence is not yet understood scientifically.
   It has been suggested that certain innate aptitudes are important for
mastering board games such as chess, Go, and awele. Two prime candidates
are general intelligence, as measured by the overall score in intelligence tests
(also known as IQ tests), and visuo-spatial abilities. Indeed, intelligence could
impact on skill acquisition in different ways. Highly intelligent individuals
may learn faster, and thus be able to acquire game-specific patterns and
methods more rapidly than less intelligent individuals. They may also search
the problem space more efficiently, and evaluate positions more accurately.
If this were so, we might expect board-game players to be more intelligent
than the general population, and more intelligent individuals to become
better players. By contrast, several researchers of expertise have downplayed
the potential role of innate intelligence in the acquisition of skill in a board
game such as chess (e.g., Ericsson & Charness, 1994).
   Alternatively, the direction of causality could be that playing board games
has a positive influence on intelligence. We have already addressed this
question in Chapter 8, where we gave a rather negative answer. The evidence
we considered then consisted of instruction of relatively short duration,
and it is a plausible possibility that the benefits of playing a game can be seen
only with longer periods of practice.
   These alternatives—intelligence affects game playing, and game playing
affects intelligence—are often difficult to disentangle, because the available
data come mostly from quasi-experimental designs. It is therefore not sur-
prising that studies addressing these issues have provided mixed answers. We
will review the available data first by considering general intelligence, and
then by dealing with visuo-spatial ability. In both cases, we first discuss the
data concerning children and teenagers, and then those concerning adults.
                                                    Individual differences    173
Intelligence in chess

Children and teenagers
As we have seen in Chapter 8, Frank and d’Hondt (1979), in their one-year
study of the effect of chess teaching, randomly allocated 90 teenagers either
to a chess class or a control class. They administered a number of psycho-
metric tests, both before and after the intervention. A correlation between
some of the pretest scores and chess skill at one year would suggest that the
cognitive abilities measured by these tests help master the game, and thus
can be used to predict skill in the game. Frank and d’Hondt found such
correlations for measures of spatial aptitude, numeric ability, administrative
sense and office work (see Chapter 8).
   Two other studies found correlations between measures of intelligence and
chess skill, but the data, unlike the previous study, are strictly correlational,
and thus harder to interpret. Horgan and Morgan (1990) found that the 15
best chessplayers in their sample (mean age around 11 years) scored higher
than the age-relevant norms on the Raven’s Progressive Matrices (an intelli-
gence test measuring reasoning and ‘pure’ intelligence) and on the Piagetian
plant task (a task aimed at measuring children’s ability to use combinatoric
logic in formal operations; see Kuhn & Brannock, 1977, for details). Frydman
and Lynn (1992) studied the mental abilities of 33 young Belgian chessplayers
(about 11 years old) using the French version of the Wechsler Intelligence
Scale for Children, a widely used IQ test. They found that their sample had a
higher general IQ than the population mean, as well as a higher performance
IQ and a higher verbal IQ (the performance IQ was higher than the verbal
IQ). Finally, the stronger players had higher performance IQ scores than the
weaker players.
   A further ability often associated with intelligence is ‘metacognition’—
the ability to monitor and regulate one’s own cognition. Horgan (1992)
addressed this question by asking participants, who were given a sequence of
hypothetical results in a chess tournament, to predict their performance
against future opponents. The results indicated that chessplaying children
performed better than their (nonplaying) parents or even statistics students.
They were also better at making predictions in a nonchess domain (tennis).
(Reynolds, 1992, and Saaty & Vargas, 1980, addressed two other aspects of
prediction in chess: the identification of players’ level given one of their
games, and what players’ behavioural and technical characteristics predict the
outcome of a championship match.)


Adults
Two studies have examined whether intelligence and chess skill are associated
in adult chessplayers. We have already mentioned that Djakow et al. (1927)
took advantage of the tournament of Moscow in 1925 to study a group of
174   Moves in mind
eight of the best grandmasters of the time and compare their performance
on psychometric tasks with a control sample made of nonplayers. Except
for some visuo-spatial tasks related to chess (see below), they did not find
any differences. In the second study, Doll and Mayr (1987) compared the
performance of chess masters with that of nonplaying students on the
Berlin Structural Model of Intelligence Test. They found that the masters
reliably obtained better scores on the aggregate score measuring general
intelligence, and in tasks related to ‘information-processing capacity for
complex information’, ‘working speed’, and ‘numerical thinking’.


Visuo-spatial abilities in chess
Given that chess is a domain in which both vision and space play an impor-
tant role, a natural hypothesis is that visuo-spatial abilities should correlate
with skill, either because practice with the game helps develop these abilities,
or because these abilities are a prerequisite for reaching a high level of skill.
Surprisingly, the existing data are far from being conclusive.


Children and teenagers
As we have just seen, Frydman and Lynn (1992) found a correlation between
chess skill and performance IQ. Taking for granted that the performance
IQ scores offer a valid measure of visuo-spatial ability, Frydman and Lynn
concluded that ‘high-level chess playing requires good general intelligence
and strong visuo-spatial abilities’ (1992, p. 235). This possibility has to be
qualified by the fact that performance IQ also includes measures not related
to visuo-spatial ability, such as alertness to essential detail, visuo-motor
coordination, concentration, logical thinking, the ability to work under time
pressure, and even verbal components (e.g., Anastasi, 1988; Mackintosh,
1998). As noted by Waters, Gobet, and Leyden (2002), the data presented
by Frydman and Lynn (1992) do not allow one to determine which specific
performance subtests, or groups of subtests, contributed most to chess-
players’ superiority.
  In a study contrasting children and adults’ as well as novices and chess
experts’ memory, Schneider et al. (1993) examined recall for visuo-spatial
material. The task measured memory for the location of wooden blocks of
different shapes. The blocks were placed on a board containing 48 fields,
which had different geometrical shapes (e.g., triangles, circles). The board
and the blocks were presented for 10 s on each of five successive trials.
The results indicated that there was no effect of expertise and age in the
first trial, but that across trials, experts improved more than novices. This
outcome is consistent with Frank and d’Hondt’s (1979) results, which,
as we have seen above, showed that the ‘spatial aptitude’ subscale from
the Primary Mental Abilities test correlated with chess skill after one year of
instruction.
                                                   Individual differences 175
Adults
As we have seen, Djakow et al. (1927) did not find any difference between
chess grandmasters and nonplayers in various psychometric tests, including
tests addressing visuo-spatial memory. The only exception consisted of recall
tasks where the material was related to chess. Grandmasters showed some
superiority in memory recall when an 8×8 matrix with moving spots was
used, and a clear superiority when chess pieces were used. Recent studies have
confirmed the lack of general, but the presence of domain-specific visuo-
spatial abilities with chessplayers. In a same-different detection task, Ellis
(1973) found that chessplayers were better than nonplayers when boards con-
tained chess pieces, but not when they contained dots. In an unpublished
study by Lane (mentioned in Cranberg & Albert, 1988, p. 161), no reliable
correlation was found between chess skill and performance on a visuo-spatial
task (the Guilford-Zimmerman Spatial Visualization Subtest, Form B; Guil-
ford & Zimmerman, 1953). Lane and Ellis used a sample of players ranging
from novices to strong amateurs.
   Two studies including masters support the conclusion of a lack of general
visuo-spatial ability. Although they did find skill differences in several tasks
measuring intelligence, Doll and Mayr (1987) did not find any masters’
superiority in a visuo-spatial task taken from the Berlin Structural Model
of Intelligence Test. Similarly, Waters et al. (2002) found no evidence for
a correlation between chess skill and visual memory ability in a group of
British chessplayers, which ranged from class D players to grandmasters.
Moreover, chessplayers did not differ from nonplayers in this task. Waters
et al. used the Shape Memory Test (MV-1) of the ETS Kit of Factor-
Referenced Cognitive Tests (Educational Testing Service, 1976).


Discussion of chess data
In sum, the pattern of results we have reviewed is puzzling. With children,
there is good evidence supporting a correlation between chess skill and
intelligence. More specifically, chessplaying children performed better on
some psychometric tests than age-relevant norms would predict; strong
child players performed better than weaker players on some of these tests;
and performance on certain psychometric measures could prospectively
predict chess skill. However, with adults, the strength of the relationship was
not as clear, with Djakow et al. (1927) finding no differences between chess
masters and nonplayers when the material was not related to chess, while Doll
and Mayr (1987) found relatively clear differences. Within the adult chess
population, there was no evidence of a correlation between chess skill and
intelligence. With respect to the association between skill and visuo-spatial
ability, the results suggest some with children, but none with adults. As
proposed by Waters et al. (2002), visuo-spatial memory, and perhaps even
visuo-spatial intelligence, may not constitute crucial factors in the long-term
176     Moves in mind
acquisition of chess skill. In any case, there are not enough data available
to draw clear-cut conclusions about which components of intelligence are
engaged in chess skill.
   All the above data (except Frank & d’Hondt’s study) are based on quasi-
experimental designs, and therefore on correlations; this makes conclusions
about the direction of causality highly tentative. There exists an indefinite
number of causal models that can account for such correlations. Among
the simplest of these models, one can mention: both chess skill and high IQ
are caused by higher motivation, the ability to cope under time pressure, or
family environment. This issue is hard to resolve, because it is difficult, if
not impossible, to carry out ideal experimental studies on this question (see
also Chapter 8). In addition, intelligence is a many sided and controversial
psychological construct (Waters et al., 2002).


Other games

Go
Masunaga and Horn’s (2000) study, as mentioned earlier, explored the
relationship between skill in Go, intelligence, and aging. They submitted
263 male players spanning 48 levels of expertise (from beginner, 30 kyu, to
grandmaster, 9-dan) to a number of tests, which were presented both in a
domain-independent version and in a Go-specific version. In the domain-
independent version, two tests measured the speed component of intelli-
gence: a search for a particular Japanese letter in a page containing 600 such
letters, and a comparison of pairs of strings of Japanese letters to decide
whether they were the same. Four further tests measured fluid intelligence:
finding the best path in a maze, recalling a set of numbers in reverse order
of presentation, selecting a figure in which a dot had the same topological
relation as in the target figure, and completing a series of letters. The Go tests
attempted to be isomorphs of the tests in the game-specific domain.
   As we have seen in the previous chapters, there was a skill effect for all of
the Go-specific tasks. By contrast, none of the general tests showed a skill
effect. Interestingly, the tests measuring intelligence speed and the series
completion task correlated relatively well (about 0.43) with the corresponding
Go-specific tasks. Masunaga and Horn suggest that the former tasks relate as
well to Go abilities as to the general abilities they measure.


Awele
Retschitzki et al. (1986b) proposed that, in order to be a good awele player, it
is necessary to have both general intellectual abilities and specific knowledge
related to the game. There is evidence that anticipation plays a central role
and that good players use hypothetico-deductive reasoning, thus supporting
the data reported by Cole and his colleagues about players of another awele
                                                    Individual differences   177
variant played by Kpelle adults in Liberia (Cole et al. 1971). In order to
identify the cognitive differences between the best awele players and the
others, a set of tasks was presented to 38 boys selected on the basis of their
knowledge of this game (Retschitzki et al., 1984; Retschitzki, Loesch-Berger,
Gut, & Brülhart, 1986a). The results show that the superiority of good
players is related neither to memory capacity nor to exceptional abilities in
quantity estimation or arithmetic. The difference of efficiency among players
seems mainly due to specific knowledge about the game acquired through
practice.
   As a result, we can reject the hypothesis that expert play is based only on
‘memory retrieval of good moves’, as argued by Béart (1955). Béart had
learned the game well enough to challenge other western people or ‘advanced
Africans’; but he lost systematically when opposed to an ‘honest farmer who
had never left his village’. He inferred that these better players (usually old
farmers) had stored all possible game situations, associated with the best
move. Béart also argued that these farmers knew many masters’ games and
were always able to control the game in order to develop one of these variants
(Béart, 1955, p. 485).
   Retschitzki (1989, 1990) concluded that players use ‘formal thinking’
during play, for several reasons: (a) the analysis of ‘awele problems’ (see
Chapter 7) shows that simple models are unable to account for the results of
the best player; (b) verbal reports by adult players (see Chapter 6) indicate
a similarity with reasoning exhibited by players of other (Western) board
games; according to their accounts, players never randomly choose the next
move; (c) analyses of game situations by Ivorean adult players illustrate that
anticipation and hypothetico-deductive reasoning occurs when considering
the choice of a move; and (d) the computer programs available at the time of
his study exhibited a very poor level of play, indicating indirectly that the
game is more complex than the simplicity of the rules suggests.


Mathematical ability
As evidenced by the claims that board games foster the development of
mathematical skills (see Chapter 8), there is a strong popular belief in a
correlation between skill in board games and mathematical abilities. De
Groot (1946) addressed this question by compiling a list showing the pro-
fession and educational level of 55 grandmasters. The results suggest that,
while mathematicians show an increased interest in chess, they are not
necessarily better at it. It is unlikely that de Groot’s results are still valid
today, for the simple reason that many grandmasters have left their academic
studies early to become professionals. De Voogt (1995) provides similar
statistics for a century of bao masters. With this game, on the surface a more
mathematical game than chess, experts did not show any resemblance
in educational, professional, social or other background, let alone in
mathematical ability.
178   Moves in mind
Intelligence and visuo-spatial abilities: Conclusion
At the beginning of this chapter, we mentioned two extreme explanations of
expert behaviour, one based on nature and stressing the role of hereditary
differences, and the other based on nurture and emphasizing the importance
of the environment, through practice. The fact that chessplayers tend to have
higher IQ scores offers some support to the first explanation, but the absence
of better visuo-spatial abilities must be seen as negative evidence. The verdict
was clearer in Masunaga and Horn’s (2000) study, where, in spite of a large
sample, there was no correlation between Go skill and a number of measures
of intelligence. No such correlations were found in awele either. In any case, it
is debatable whether the nature/nurture opposition is tenable scientifically;
rather than attempting to prove that either position is better, a more
profitable endeavour is to offer detailed mechanisms explaining how nature
interacts with nurture in the long developmental path leading to expertise
(Gobet & Campitelli, 2002).


Personality
Several studies have tried to identify correlates of successful competitive
chessplayers. Kelly (1985) administered the Myers-Briggs Type Indicator,
a questionnaire aimed at measuring Jungian personality characteristics,
to American players ranging from novices to grandmasters. Chessplayers
scored higher than the general population on the introversion, intuition,
and thinking scales; stronger players also scored reliably higher than weaker
players on the intuition scale. Avni, Kipper, and Fox (1987), using the
Minnesota Multiphasic Personality Inventory, found that chessplayers dif-
fered from the control group in measures of orderliness and unconventional
thinking; highly competitive players were also significantly more suspicious
than nonplayers. As testosterone is linked to aggressiveness in several primate
species, Mazur, Booth, and Dabbs (1992) used this measure to estimate
assertiveness and dominating behaviour in male chessplayers. As with other
sports, they found that players who tended to win in a tournament showed
higher testosterone levels than players who tended to lose, and that some
competitors showed a rise of testosterone level before their games, perhaps as
a way to prepare themselves for the contest. Joireman, Fick, and Anderson
(2002) found that people scoring high on a measure of sensation seeking were
more likely than those scoring low to have played chess, and also to have more
experience with the game.


Emotions and motivation
There are few empirical data available about the role of emotions and
motivation in board games, and even fewer about their relation to cog-
nition. Cleveland (1907) briefly addressed the question of emotion in the
                                                   Individual differences   179
development of chess expertise, but did not present any concrete data.
Such data were provided by Tikhomirov and colleagues. In one experiment
(Tikhomirov & Vinogradov, 1970), the galvanic skin response (GSR) was
recorded. Results indicated that players show an increase in GSR at the
critical points of their problem-solving activity. Players were also taught to
regulate their GSR level by controlling their emotions when solving chess
problems. That they could do this is evidenced by the flat GSR they could
maintain, which indicates stable affect or arousal. In this apathetic emotional
state, they were still able to solve problems of medium difficulty, but
were unsuccessful with the more difficult ones. Tikhomirov and Vinogradov
suggest that some degree of emotional arousal is necessary for efficient
cognition.
   Tikhomirov (1990) also reports the use of hypnotic techniques to bolster
chess skill (see also Hartston & Wason, 1983). Tikhomirov and Vinogradov
(1970) sketch a theory where heuristic phenomena in chess are explained by
a complex interaction of emotional and cognitive processes. In particular,
emotional activation fulfils an important regulatory function, which is
needed for productive intellectual activity.
   Gobet (1986, 1992; Gobet & Retschitzki, 1991) attempted to induce
emotional and motivational changes experimentally and to study their effect
on problem solving. The goal was to explore the possibility of inducing
‘learned helplessness’ in chessplayers of different skill levels. Learned help-
lessness (Seligman, 1975) refers to cognitive, emotional, and motivational
deficits produced by the lack of contingency between an organism’s
responses and the outcomes of the environment; in extreme cases, these
deficits may lead to depression. Gobet and Retschitzki addressed three
questions: can a mild form of learned helplessness be induced with a treat-
ment involving a cognitive task, as opposed to an instrumental task? How
does skill mediate the effect of noncontingency? And, does the similarity
between the tasks used during treatment and posttest play any role?
   The experimental design comprised three groups. Players in the first group
faced chess positions that had an objective solution and received correct
feedback; positions were presented for 30 s, and two solutions were proposed.
Each member of the second group was given positions without objective
solution, and received the same feedback as the member of the first group
he was yoked with (thus, there was no correlation between the answer and
the feedback). Finally, the control group carried out a task not involving
responses and feedback. Players’ performance was then assessed in two
posttests, one similar to the treatment, the other consisting in a different,
longer task (selection of the best move in de Groot’s Position ‘A’; see Chapter
6). A self-report inventory was administered before and after the experiment
to measure possible emotional changes. Participants were 48 Swiss players,
ranging from 1600 to 2450 Elo. While the group with nonveridical feedback
did not perform as well as the other two groups in the posttest similar to
the treatment, there was no reliable difference in de Groot’s task. Thus, the
180   Moves in mind
effects were proportional to the degree of similarity between the treatment
and the posttest. Results also indicated that, at the end of the experiment, the
members of the treatment group had higher depressivity scores than the two
other groups. In general, the average-strength players were the most sensitive
to the manipulation, and the weakest players were not affected. The final
result was unexpected, but hinted at some benefits associated with board
games. At the end of this rather demanding experiment, all skill groups
showed a decrease in tiredness. As Gobet (1992, p. 42) put it: ‘Even when it is
part of a psychological experiment, chess players really seem to find the game
relaxing!’
   While the previous experiment studied the effects of lack of control,
Fleming and Darley (1990) addressed the question of ‘illusion of control’.
They were interested in the features that may lead observers to believe that
individuals have exerted control over a random event. Observers read stories
about a game of backgammon where players either strongly wished a specific
outcome for the roll of the dice or were indifferent. The dice were rolled either
by the players or a third party. Results indicated that observers were more
likely to (incorrectly) infer that the players had exerted control over the roll of
the dice when the players desired a particular outcome and had rolled the dice
themselves.


Board games and neuroscience

A theory of the neurobiology of chessplaying
In their review of the then available evidence on the neurobiology of
chess skill, Cranberg and Albert (1988) used as a framework Geschwind
and Galaburda’s (1985) influential theory of the neuro-anatomical
substrate of talent. We will refer to the same framework, as it con-
veniently organizes data which would otherwise seem disparate. A brief
description of this theory is followed by a discussion of how well it
accounts for data about gender differences, handedness, brain lesions, and
brain imaging.
   Geschwind and Galaburda’s (1985) ambitious theory aims to explain a
complex pattern of results linking, among other things, brain lateralization,
dyslexia, proneness to allergies, talent in visuo-spatial domains (e.g., chess,
mathematics), and handedness. Given that the theory is rather complicated,
we can give here only a brief overview of its main components. Starting
from the widely accepted premise that the right hemisphere of the brain
normally underpins visuo-spatial abilities, Geschwind and Galaburda
reasoned that better development of the pattern of cortical connections of
the right hemisphere should lead to better performance in visuo-spatial tasks.
But what factors could affect this development? Geschwind and Galaburda
propose that great exposure or high sensitivity to intrauterine testosterone in
the developing male foetus leads to a less developed left hemisphere than
                                                    Individual differences 181
usual, and, as a compensation, to a more developed right hemisphere. Hence,
there should be more males than females in visuo-spatial domains such as
mathematics and chess; similarly, as the left hand is connected to the right
hemisphere of the brain, lefthanders should be better represented in these
fields than in the general population. Geschwind and Galaburda’s theory
thus makes rather clear predictions, some of which can be tested with a
variety of data from board-game research.


Gender differences in chess
Chess has not always been characterized by a male superiority. Murray
(1913) reports that, in the Middle Ages, both genders were playing chess at
an equal level. But Geschwind and Galaburda’s prediction of a superiority of
males over females is verified in the last two centuries. For example, there is
currently only one female in the 100 best players in the world (Judit Polgar,
who, in July 2003, was ranked number 11 in the world with an Elo of 2718).
Some other theories have attempted to explain this striking superiority (see
Dextreit & Engel, 1981; Gobet, 1985; Hartston & Wason, 1983, or Holding,
1985, for reviews): theories based on psychoanalytical premises (e.g.,
Fine, 1967); on intelligence differences between males and females; and on
difference in upbringing.
  Before deciding between these alternatives, Charness and Gerchak (1996)
recommend considering the total numbers of females and males playing
chess. They show that a simple mathematical model, taking into account
the total number of players, accounts for the respective numbers of high-
ranked female and male chessplayers. Still, the question remains why this
total number is lower for females than for males; Charness and Gerchak
remain neutral on this point, mentioning that this can be explained by one of
the theories we have mentioned above.
  There is at least one data point directly supporting the role of the environ-
ment. Three Hungarian sisters (the Polgar sisters) were trained early on by
some of the best Hungarian grandmasters, and competed almost exclusively
in ‘male’ competitions. All were highly successful and two obtained the
grandmaster title with the requirements usually demanded for male players.
As we have seen, Judit Polgar, the youngest of the three, is ranked amongt the
best players in the world. As there is no evidence that they came from a
particularly gifted family or that they excel in other domains, it is reasonable
to take this ‘natural’ experiment as supporting the important role of the
environment in developing chess skill.


Gender differences in other board games
Contrary to the situation with board games in Europe and Africa, East Asia
has produced a large number of women masters. Gender differences are
not considered obvious in the game of Go or even in the games of shiang qi
182   Moves in mind
(Chinese chess) and shogi (Japanese chess). This discrepancy is mostly his-
torical and not psychological, although sound research on this topic is still
wanting. It appears that Go and shogi were played at high levels in Japan
as of the beginning of the seventeenth century. When shogi became a game
of gambling and therefore unsuitable to women, the level of women shogi
players dropped accordingly. The literature on women masters in China and
Japan consists mostly of (auto)biographies and books concerning strategy
which are written by these women masters or their organizations. In addition,
there is the occasional history book (Hayashi, 1975; Juan, 2000).
   For shiang qi we should mention the biography and strategic analyses by
Dan and Xu (1998). Shogi women players are less strong but also produce
autobiographies (e.g., Hayashiba, 1993) and numerous strategy books.
Women Go masters have been equal to their male counterparts for
much longer; an overview for Japanese players is given in Nihon Ki-in
Joryuukishikai (1999), in addition to the books written or compiled by
women players themselves such as the book by Nakayama (2000) or by Go
clubs such as Igo Kurabu (1983). The Chinese players are mentioned in one
of the few English language books by a women master (Juan, 2000). To this
we can add numerous biographies such as that by Ri and Jiang (2001),
and strategy books such as those by Li (2001). Chinese international
chessplayers are also productive writers (e.g., Lin, 1999), just as the Polgar
sisters (Polgar & Shutzman, 1997).
   In the West, the competition for men and women has almost always been
separated. In international draughts, occasional women champions have
beaten one or two former world champions, but this has not been a regular
occurrence. In international chess, the women’s league, which is dominated
by Chinese and Russian players, rarely interacts with the men’s league,
although there has been a trend in recent years for the women to play in
traditionally male tournaments. The success of the Polgar sisters and the
large contingent of women masters in Go, both in China and Japan, at least
makes further comparative research on expertise possible.


Handedness and chess
Geschwind and Galaburda’s theory (1985) also predicts that the proportion
of people who are not righthanders should be higher in the chessplaying
population than in the general population. The limited available data support
this prediction. Cranberg and Albert (1988) sent a questionnaire to about
400 players belonging to the US Chess Federation ranking list. They targeted
the two extremes of the distribution, i.e. the 200 best players (Elo rating >
2250), and the 200 weakest amateurs (Elo rating < 1275). In the question-
naire, players were asked to classify their handedness in one of four options:
righthanded, lefthanded, ambidextrous, or lefthanded as a child and later
switched to righthanded. About 260 players answered—which is a rather
good response rate. Of the male chessplayers, 18% were not righthanders.
                                                     Individual differences 183
This percentage differs reliably from that in the general male population,
which has been estimated to lie between 10 and 13.5% (Bryden, 1982). Inter-
estingly, there was no difference between the group of strong players and
the group of weak players, even though they were separated by more than five
standard deviations. The female chessplayers did not differ from the general
female population (from 6 to 9.9%; Bryden, 1982).
   Cranberg and Albert (1988) used a rather informal method to measure
handedness. In a replication, Campitelli and Gobet (2003) improved on the
methodology by employing a well-validated questionnaire, the Edinburgh
Handedness Inventory (Oldfield, 1971). This questionnaire was given to
101 male players in Buenos Aires, ranking from 1490 to 2473 Elo. The
results closely replicated the previous study: 17.9% of the chessplayers
were nonrighthanders. Again, there was no difference between strong and
weak players.

Effects of brain lesions on chess skill
A direct consequence of Geschwind and Galaburda’s theory is that chess
skill should be impaired more by lesions to the right hemisphere of the brain
than by lesions to the left hemisphere. Cranberg and Albert (1988) report
data about eight unfortunate chessplayers who suffered brain damage. Even
after large left-hemisphere lesions, the ability to play chess was preserved.
Moreover, minor right-hemisphere lesions did not affect chess skill. This
study is inconclusive, however, because no evidence was presented about the
effect of large right-hemisphere lesions, the type of lesion directly addressed
by the theory.


Brain activity in chess and Go
Geschwind and Galaburda’s theory implies that chessplaying should produce
more brain activation in the right hemisphere than in the left. Chabris and
Hamilton (1992) performed a divided visual-field experiment with male
chessplayers. In this type of experiment, patterns (here, patterns of chess
pieces) are briefly presented to the left or right of a fixation point; this enables
the experimenter to control where the pattern appears in the retina of the
right and left eye. Because of the anatomy of the human visual system
between the retina and the visual cortex, this methodology also enables one
to control what is processed in either the right or the left hemisphere. Chabris
and Hamilton’s results suggest that the right hemisphere is better than the
left at parsing according to the default rules of chess chunking, but that
the left hemisphere is better than the right at grouping pieces together when
these rules are violated.
   Hatta, Kogure, and Kawakami (1999) were also interested in hemisphere
specialization. They submitted Go experts and novices to a visuo-spatial
memory task where digits placed in cells were projected either to the left or
184   Moves in mind
right visual field. Whereas no clear group differences were found in identify-
ing the digits and locations with four digits in six cells, differences became
apparent with four digits in 16 cells. Go experts were more accurate than
novices. For number identification, both groups showed a right-visual field
laterality. For location identification, Go experts did not show any visual
field preference, while novices showed an advantage for the right-visual field.
Note that this study also demonstrates that skill in a specific domain (Go) can
transfer to another visuo-spatial task.
   Volke, Dettmar, Richter, Rudolf, and Buhss (2002) recorded the electro-
encephalogram (EEG) of chess experts and novices when they performed
simple tasks with chess stimuli. In the more complex tasks (check detection,
checkmate judgement, and mating in one move), the experts showed a more
posterior pattern of brain activity, while the novices showed a higher acti-
vation in frontal areas. Experts showed more activity in the right hemisphere
and displayed a greater coherence in their EEG signals.
   Several brain-imaging techniques have been employed with chess and Go.
Using positron emission tomography (PET), Nichelli et al. (1994) studied 10
righthanded males, who had been playing chess for more than 4 years. Simple
tasks were used, such as black/white discrimination, spatial discrimination,
rule retrieval, and checkmate judgement. The results show that these tasks led
to the activity of a network of interrelated, but functionally distinct, cerebral
areas. There was no evidence supporting a predominant role of the right
hemisphere. The tasks may have been too simple to address chess expertise.
   Onofrj, Curatola, Valentini, Antonelli, Thomas, and Fulgente (1995) used
single photon emission computerized tomography (SPECT) to study brain
activation in a more complex task: solving a chess problem. A limit of this
study should be mentioned at the outset: only one position, taken from the
game Lasker-Bauer, Amsterdam, 1889, was used, a ‘classic’ that is likely to
have been known to the players. Onofrj et al. found a nondominant activation
in the dorsal prefrontal cortex, as well as a lower nondominant activation in
the middle temporal cortex. These results are consistent with previous
brain-imaging research: typically, the dorsal prefrontal cortex is activated in
problem-solving activities involving planning, and the right mid-temporal
lobe is activated during memory retrieval of nonverbal information. As
predicted by Geschwind and Galaburda, the four righthanders displayed
activation in the right hemisphere. Contrary to what their theory would
predict, the only lefthanded player of the study displayed similar activation in
the left hemisphere, and not in the right hemisphere.
   Amidzic, Riehle, Fehr, Wienbruch, and Elbert (2001) conducted a study
with the ‘gamma-burst’ technique. Twenty chessplayers, ranging from class B
players to grandmasters, participated in the study. The task was to play a
chess game against a computer. During the game, players were scanned 5
seconds after each computer move. Amateurs showed a pronounced activity
in medial temporal structures (i.e., perirhinal and entorhinal cortex, and
hippocampus) relative to the activation in parietal and frontal areas. With
                                                    Individual differences 185
masters, activation was strong in the frontal and parietal lobes. No difference
in the laterality of brain activation is mentioned in this study, but Amidzic et
al. speculate that the structures identified with the amateurs play only a
transitional role during the encoding of chunks in the neocortex.
   Atherton, Zhuang, Bart, Hu, and He (2003) performed an fMRI study with
chess novices. In the game condition, the task was to find the best move
for white; in the random condition, the task was to identify pieces marked
with a star; in this condition, the pieces of a game position were randomly
shuffled throughout the board and were also positioned randomly within a
given square. The contrast between brain activation in the random and game
condition revealed activation in the frontal, parietal and occipital lobes. In
general, the left hemisphere was more active than the right.
   Chen et al. (2003) describe a Go fMRI study which used the same design as
Atherton et al. (2003). Their subjects all had a Go rating, which make them
stronger than the chess novices studied in Atherton et al. The same areas were
activated as in the chess study. In addition, posterior temporal areas as well
as primary somato-sensory and motor areas were activated. There was a
tendency for a stronger activation in the right parietal area than in the left.
   Campitelli (2003) performed three fMRI experiments with chessplayers.
The first investigated autobiographical memory, and the other two examined
the role of expertise in memory. One grandmaster and one international
master participated in the study on autobiographical memory. Three types
of stimuli were used: positions from games the two participants had played
(obtained from a database); positions from games by other masters; and
nonchess control stimuli. In the fMRI scanner, the task was simply to look
at each position for 5 s. Four hours later, the two players were asked to
provide information about these positions, and an hour after this, they
carried out a recognition task with old and new positions. The critical
contrast was the subtraction of the brain activation when looking at
others’ positions from the activation when looking at the participants’ own
positions. Both conditions were similar perceptually, and the only difference
related as to whether participants’ own positions elicited autobiographical
memories. The high performance in the recognition task suggests that this
was the case. The contrast showed a pattern of brain activation in the left
hemisphere, similar in both players, including frontal areas and posterior
parietal areas.
   In the second experiment, chessplayers and nonplayers performed a task
with and without chess stimuli, in which a position had to be maintained in
memory. In addition, there was a control task in which chess stimuli were
used, with no requirement of memory. When the activation in the control
task was subtracted from that in the memory task with chess stimuli,
nonplayers exhibited a much greater activity in frontal and parietal areas
than chessplayers. These areas are related to working memory processes,
suggesting that nonplayers needed more effort to maintain a position in
working memory. In the contrast between chess stimuli and nonchess stimuli,
186   Moves in mind
chessplayers displayed a pattern of activation in medial temporal areas,
which are thought to be involved in long-term memory storage. The
third experiment was a follow-up of the second, and suggested that it is
the semantics of the chess pieces, and not the perceptual appearance of
the stimuli, which accounts for the differences between chess stimuli and
nonchess stimuli observed in the second experiment.


Board games and neuroscience: Conclusions
This section has discussed the biological basis of board-game skill, of which
little appears to be known. Geschwind and Galaburda’s theory received
mixed support, faring well with the questions of handedness and gender
differences in chess, but less well with the questions of gender differences in
other board games, and with brain-imaging data. The brain-imaging studies
suggest that frontal and posterior parietal areas, among other areas, are
recruited for chess and Go. These areas are known to be engaged in working-
memory processes (e.g., Roberts, Robbins, & Weiskrantz, 1998). Neuro-
science research is progressing rapidly, and it is likely that, in the near future,
new results can be expected on the biological mechanisms enabling expert
behaviour—be they the reflection of strong innate individual differences,
the effect of later biological developments (as in Geschwind and Galaburda’s
theory), or the mechanisms enabling dedicated study and practice.


Conclusion
This chapter has raised more questions than it has provided answers.
While the role of intelligence for board games can at least be addressed
with empirical data, little is known about the role of emotions and moti-
vation. This is clearly a domain in which active research should be pursued.
Similarly, there is little robust evidence from neuroscience research, and,
given the novelty of the techniques used, the need for replication is apparent.
Theoretical links were sometimes made between neuroscience and the
chunking theory, which has dominated the previous chapters of this book
(e.g., by Amidzic et al., 2001; Chabris & Hamilton, 1992), but these links
should be seen as highly tentative at the moment. Connecting neuroscience
with cognitive theories such as the chunking or template theories is likely to
be an active domain of research in the near future.
   The topics discussed in this chapter raise intricate methodological
questions. For example, how can the direction of causality between expertise
in board games and intelligence be ascertained? What is the best way of
measuring brain activation differentiating search and pattern-recognition
behaviour? Obviously, this is not the only place in this book where
methodological issues are raised. In the following chapter, we reflect on the
methodological strengths and weaknesses of research into board games,
and how they may shape future research.
10 Methodology and
   research designs




The previous chapters have described the current state of research into board
games, both empirically and theoretically. The goal of this chapter is to revisit
this research from a different angle by critically discussing its methodology.
Although chess will often be treated as an implicit gold etalon, we shall
see that other games often have characteristics that open new research
opportunities.
   We first deal with general questions such as the definition of expertise,
game specificity, ecological validity, and cross-cultural considerations. We
then discuss the question of notational systems and archives, which has con-
sequences for the design and interpretation of psychological experiments.
Next, we review the empirical techniques used, considering in turn observa-
tion, interviews, questionnaires, introspective reports, protocol analysis, and
experimental techniques, including recent methods from the neurosciences.
A broader view follows, where we consider the classes of empirical designs
employed (either cross-sectional or longitudinal). After dealing with formal
methods, we will be in a position to evaluate the methodological strengths
and weaknesses of board-game research.


Definitions of expertise
While the notion of expertise is readily understood by laypeople—experts are
individuals who excel in a domain—it is harder to provide a precise definition
(e.g., see the contributions in Ericsson, 1996). Richman et al. (1996) propose
that an expert can be defined pragmatically as someone performing at the
level of an experienced professional. Often, researchers use criteria such as
academic qualifications or seniority, although these criteria, which are not
based on objective measures of performance, are imprecise at best and irrele-
vant at worst. Compared with other domains of expertise often studied in
psychology (e.g., medicine, physics, programming), board games have the
crucial advantage of being competitive. Therefore, skill comparison is an
inherent characteristic of the domain: if researchers wish to determine which
players are experts, they can use tournament results.
188   Moves in mind
Titles and ratings
In several board games, titles are awarded to strong players as a function of
tournament results (chess; cf. Elo, 1978) or examinations (Go; cf. Masunaga
& Horn, 2000). The shortcoming of the title system is that it measures only
the best performance of an individual, and does not take into consideration
possible losses or fluctuations. Some board games (chess, Othello, checkers,
international draughts) are fortunate to use, in addition to a title system,
quantitative measures, notably the Elo rating (Elo, 1978).
   Since its introduction in 1952 by the US Chess Federation, the Elo rating
has been increasingly used by the chess community and an array of other
Western board games, including games exclusively played over the Internet.
The Elo system, which is based on sound mathematical footings, computes
the rating of a player as a function of both the outcome of a game (win, loss,
or draw) and the strength of the opponent. (For a derivation of the system
from the theory of probability, see Batchelder & Bershad, 1979; Elo, 1978; or
Glickman, 1995.) Such a quantitative measure of skill is almost unique in
expertise research: in other domains studied in psychology, such as medicine
or physics, researchers have to content themselves with rough categories such
as ‘novice’, ‘intermediate’, and ‘expert’.


Informal definitions of expertise
In the case of less organized board games or games for which there are not
enough masters or tournaments to set up an Elo rating system, there are
other ways of distinguishing experts from novices. A first indication is the
consensus among players. If all agree on a ranking, then this provides strong
guidance to the researcher. Although anecdotes cannot be considered an
accurate measurement for mastership, they may provide the opportunity for
several historical and international comparisons. Notably, if there have been
international championships and the current masters participated and won,
then the mastership of the present set of masters gains in credibility. A con-
sensus of this or any other kind is more accurate than the last tournament
result, which may suffer from fluctuations in players’ performance. Moreover,
it may be difficult to compare the outcome of several tournaments without a
formal method such as the Elo system.
   A second method of rating players is the experiment itself. For example, de
Groot’s memory experiment provides results that correlate reasonably with
chess skill, assuming a range of skill wide enough (e.g., Waters et al., 2002,
found a correlation of 0.68). A limitation of this approach is that perform-
ance in an experiment does not always reflect performance in a game. In this
case, the outcome of an experiment can be used to make a rough selection
among players, and its inaccuracies are immediate food for further research,
since they hint on other aspects of players’ expertise.
   The final method is setting up a rating system as a researcher, i.e.,
                                        Methodology and research designs 189
organizing tournaments and keeping scores. There can only be success if the
effort continues for a number of years, an unlikely project for a psychologist,
albeit an admirable one.
   Where a game has not received international recognition, there is an
additional problem of scepticism. Even if some players are the best, whether
shown through ranking or consensus, why should they be considered
masters? Would an outsider with a few years of training be better than these
players? This brings forward a consensus that already exists for chess and
other familiar games. As soon as people have tried themselves, in order to
have the ability to appreciate the efforts of others, and as soon as they are
impressed by certain feats, only then may they consider the term mastership.
It is therefore not unlikely that the best way to determine mastership is
to identify accomplishments out of reach for people who practise for a few
years.
   In a tournament, the analysis of important games may provide material to
convince the sceptics, but experiments play a more convincing role than these
analyses if the game is not understood. In the case of illiterate board games
(see below), the audience in psychology is nearly always unfamiliar with the
game. Without setting up a rating system, certain anecdotes and examples
may already corroborate the existence of mastership and remove the problem
of scepticism.


Game specificity
Board-game experiments are typically designed in one of two ways, which are
not entirely independent. The experimenter aims either at testing specific
hypotheses from the psychological literature (e.g., effect of verbal interference
on problem solving), or is guided by the board-game literature. In the latter
case, the experiment is likely to incorporate features idiosyncratic to a specific
game. For example, if the literature contains position analyses and the
masters conduct such analyses in their practice, then psychologists are
tempted to design an experiment on how players analyse positions. There is
no guarantee, however, that experiments inspired by a specific board game
can be exported to other games, even with substantial changes.
   A case in point is de Groot’s (1946) chess memory experiment, which has
become a model in the field of expertise. Although this experiment has some-
times been criticized for its lack of ecological validity, and the fact that it is a
‘contrived’ task, as opposed to a natural task in the domain (Vicente & Wang,
1998), it is undeniable that it has produced interesting results not only with
chess, but also with other domains. Nevertheless, it is a legitimate question
as to whether this experiment naturally extends to other board games, and
the evidence reviewed in Chapter 5 actually indicates some difficulties with
mancala games. The difficulties do not come from the lack of documented
positions (most mancala variations are undocumented games), as it is easy
to create such positions for experimental purposes. Rather, they come from
190   Moves in mind
threats to ecological validity (see below), and from the particularities of each
game.
   While de Voogt’s (1995) bao experiment failed to replicate the memory
performance found with chess masters, this does not mean that one cannot
find other (game-specific) skills. These may be identified, for example, by
interviewing masters and by studying them for the relevance of certain skills
in the game in which they excel. In the case of bao, the calculation of duru is
a game-specific skill for which the psychologist can easily create experiments.
These experiments can highlight players’ cognitive processes and knowledge
structures, and perhaps provide results that can measure players’ skill.
   In cases such as memory performance in chess and bao, has research
become incommensurable? There are two likely outcomes to such a situation.
First, the experiments are adjusted for either game to allow comparison.
Second, the emphasis, both theoretically and experimentally, becomes dif-
ferent for the two games. For example, the chess recall task has led to follow-up
experiments about perception, such as eye-movement recordings, and to a
variety of memory experiments that have helped clarify the initial results. By
contrast, with bao, the duru experiment was followed up by short duru and
blind duru experiments to understand memory-allocation processes, and did
not address issues of perception. Since duru can only be found in bao, the
impact on experimental research is too early to be established. The logistic
complications of doing research on bao, compounded with cross-cultural
difficulties, prevent psychologists from testing bao players on other aspects of
cognition, by, for example, using eye-movement recordings.


Illiterate games
If there is no commonly used notational system to record moves, one can
qualify such a game as ‘illiterate’. If this is the case, the researcher is limited in
the archival access to games. If the players themselves are illiterate in one or
any notational system, then researchers are limited in the type of experiment
they can carry out.
   The influence of board-game literacy on masters’ performance is difficult
to evaluate from the limited research on illiterate board games. It is, for
instance, possible to claim that position analysis hardly plays a role for
masters of bao, a game with no archival tradition. By the same token, it is
complicated to conduct experiments similar to those in chess that could
substantiate this claim. Before discussing the role of notational systems in
more detail, we need to address the question of ecological validity and its
relation with cross-cultural psychology.


Ecological validity
In his influential book Cognition and Reality, Neisser (1976; see also
Brunswik, 1956) spelled out several criteria that cognitive psychology should
                                       Methodology and research designs 191
strive to satisfy in order to insure a minimum of ecological validity. Research
into board games fares well in this respect. It typically studies domain-
representative tasks that belong to the ordinary environment of the par-
ticipants. It also studies the development of complex abilities, and not only
disjoint skills, as is often done in experimental psychology. Nevertheless, it
is true that some of the tasks used are not particularly ecological, and this
merits discussion.
   The use of artificial tasks does not mean that the results are not of
theoretical importance. Indeed, some of the experimental manipulations in
board research that have had much theoretical impact are arguably far from
anything done in real life: recall of random positions, interference in memory
tasks, or solving a problem when typing on a keyboard. In the case of
chess, players have been remarkably flexible in adapting to sometimes con-
trived manipulations. There are only few documented examples of players
refusing to do (part of) an experiment, such as Gobet and Simon’s (2000a)
grandmaster who refused to memorize random positions.
   If players are unfamiliar with the experimental situation, as is often the
case in non-Western cultures, then researchers have to adjust the experiment
itself, the situation in which the experiment is conducted, or the preparation of
the players for the experiment. A subtle change from a real to a hypothetical
situation, such as analysing the game of someone who is not even there
instead of one’s own game, may require considerable explanation or teaching.
   The differences in context, when unaddressed, may lead to a frustrated
performance. The most important effect is that experts may not perform at
the level of experts. In most cases, this is due to a lack of motivation, which
may be created by three common problems. First, players are not convinced
of the significance of the task or its relevance to the game. Second, they may
not be experts in that particular part of the game and may, therefore, show
a clear disinterest in performing well. And third, they are pressured by the
alien experimental situation. Solutions include the investment in time to
motivate players, the selection of tasks with which players feel familiar, and
the repetition of the task at different points in time to accustom players to
the experiment. Such solutions may limit the number of possible players
significantly, which is problematic since experts are rare. Moreover, the
player becomes trained in performing in the experiment (cf. Ericsson, 1996;
de Groot & Gobet, 1996). In that case, the experiment concerns master
‘performers’ instead of master players.
   Experts are often motivated by the fact that they will perform well or at
least better than lesser players. If it appears that they will fail or perform
badly in an experiment, they may discontinue their cooperation. If the
situation is alien or uncomfortable, their performance may be reduced to
a novice performance, with a similar effect on their motivation. Both the
researcher and the player should therefore prefer a situation close to a playing
situation. It is only in rare circumstances that motivation is not an issue, such
as where the player becomes researcher.
192   Moves in mind
Cross-cultural aspects
Motivational problems may be aggravated by language and cultural barriers,
as well as a poor understanding of the game by researchers. It is no coinci-
dence that several psychologists were masters themselves before becoming
active in research. This explains why research has concentrated on Western
board games, in particular chess. There are few, if any, Western psychologists
fluent in Chinese, masters of Chinese chess, and therefore interested in
running experiments with this game.
   Cole and Scribner (1977) suggest that familiarity with the material is
important if people are going to apply their cognitive skills. The use of
material is limited by particular cultural contexts. For example, although the
use of a computer offers several advantages in recording performance, it may
obscure players’ performance if they are not computer literate. In addition,
a certain dexterity in using the mouse has to be assumed, which can have
unwelcome consequences. These problems are not just related to using a
computer. Rayner (1958b) observed that the time taken by children under 11
in playing a move of pegity was entirely due to their sensorimotor skills, in
this case their ability to place pegs in the designated holes. This time was
not related to thinking time, unlike older players. These issues in setting up
a cognitive experiment become prominent in games such as awele and bao,
where experts and novices are often not familiar with materials other than
their own game boards.
   Inventive experimental designs may reduce the problems just mentioned,
although this reduction may seriously limit the number of experiments that
can be imported from other contexts. Apart from the absence of notation
systems and archives, the unfamiliarity with materials and even with the
notion of an experiment limits comparisons with other board games.


Creation and use of archives and databases
In some board games, players have amassed a huge amount of information:
entire games, accumulated wisdom about openings and endgames, composed
problems, and analyses. This material can then be organized and stored in
written or computerized archives. The presence or absence of archives has
significant consequences for psychological research.


Notational systems
Archives of transcribed tournament games require a game to have regular
tournaments, a notational system, and people fluent in its use. International,
Japanese, and Chinese chess, as well as Go, checkers, and international
draughts, for instance, satisfy these requirements and have such archives
available. Often games are published in annotated form after a tournament
or as part of a study of one particular master. Although literature study
                                      Methodology and research designs 193
is common for ambitious players, there have been examples where even
grandmasters were not able to read or write. In international draughts,
the legendary Baba Sy from Senegal was, at the beginning of his career,
accompanied by a ‘notateur’, the young Ton Sijbrands (later world
champion), to record his games during official tournaments. The example of
Baba Sy illustrates two important points: first, players are not always familiar
with a notational system or able to use it correctly; and, second, the lack
of familiarity with a notational system does not necessarily make them
lesser players.
   In addition to games, other records not automatically kept can be scien-
tifically enlightening. For some researchers, it may be of interest to record
information about timing, such as the average playing time, the time taken
for each move, the time spent at the board (as opposed to walking around),
and the total playing time. An average tournament with about 50 or 100
games will allow the researcher to set up an archive to illustrate a particular
aspect not considered in other archives or for a game that did not have an
archive before.
   Where players have not developed a notational system, the problems are
more complicated. Although the presence of such a system can be of benefit
in the long term, forcing players to learn one is not without shortcomings:
it may be time consuming to acquire it; players have to concentrate on record
keeping during their games; and disturbances of players’ concentration may
influence the level of play even if extra time is granted.
   Instead of forcing players to use a notation system, a more promising
approach is to make video recordings of the games. The analysis of videos
allows the researcher to record the moves and the time, as well as document
irregularities. For example, the videotaping of 92 bao games in a Zanzibar
tournament made it possible to establish the average duration of games,
both in number of moves and minutes (de Voogt, 1995). In addition, this
method allowed the detection of five occurrences of misplaced seeds; these
unintentional errors would have made it otherwise impossible to replay these
five games.


Impact on masters’ play
The existence of archives changes masters’ approach towards their game,
in particular if these archives are widely available, through either books or
computer databases. As noted in Chapter 8, these sources of information
open up possibilities to prepare for matches or to improve certain aspects of
the game. When the archives are used for analysis, at least some typical com-
binations or positions tend to receive names for future reference. In addition,
opening, middle- and endgames may be labelled, allowing players to develop
a common language, which in turn helps researchers in the preparation of
experiments (e.g., for chess, de Groot, 1946; Saariluoma, 1995). Conversely,
the absence of archives often results in a much less articulated playing theory
194   Moves in mind
and a less rich jargon at the disposal of the players, although it should be
pointed out that board games do not require the presence of an archive to
have good players.


The role of archives for designing experiments
The absence of an archive used by players may have consequences for designing
experiments. If there is no literature available to masters, it is more difficult
to find well-analysed positions ready for use. If suitable positions are found
in the researcher’s archive, it is likely that certain players too are familiar with
them while others may not be familiar at all. Researchers, when selecting
positions for experiments, have to be experts in the game themselves in order
to find suitable game positions. De Groot’s (1946) chess experiments
contained all these elements: the presence of an archive, a choice of well-
analysed positions, and the expertise of the researcher. While these elements
are useful, they are not necessary for designing experiments. Even so,
it should be recognized that their absence might make it difficult or even
impossible to replicate some experiments.
   Information available in archives can direct researchers to certain types of
experiments. A nice example is offered by Billman and Shaman’s (1990)
study. Based on a historical analysis of Othello, they suggest that strategy
change and pattern recall are linked; in particular, the introduction of a
‘mobility strategy’ in Othello directly affects recall of games. A natural exten-
sion of this study is to inform the design of experiments with historical
records of strategy changes in chess, Go, checkers, and gomoku.


Analysis of archives and databases
Once the archive is in place, the recorded games can be used for further
analysis. Archives and databases have been used to extract information about
both the environment and the psychology of board games. For example,
to study the statistical structure of the chess environment, de Groot (1946)
analysed the 300 games contained in Tarrasch (1925) and extracted measures
such as the average game length and the average number of legal moves per
position. (See Holding, 1980, as well as Rubin, 1963, 1972, 1973, for similar
analyses.)
   In similar vein, de Groot and Jongman examined 192 positions to pinpoint
statistical and informational properties of the chess environment (de Groot &
Gobet, 1996; Jongman, 1968; see also Chapter 5). These authors also used
information theory (Shannon, 1951) to estimate the total number of posi-
tions that could, in principle, occur in master games. Such a theory of the
environment is useful in that it can be used to predict human behaviour in
specific experiments, such as memory recall after a brief presentation. De
Groot and Jongman’s approach can easily be generalized to other games.
(See also the discussion of game complexity in Chapter 2.)
                                      Methodology and research designs 195
   Nowadays, computer technology makes it possible to carry out similar
analyses using hundreds of thousands of games or more. Using a statistical
analysis of masters’ games, Sturman (1996) has identified or confirmed a
series of principles and regularities about chess endgames (e.g., strength of
Bishop pairs in open positions). Nunn (1994), among others, has extracted
useful endgame principles using results from retrograde analysis (see Chapter
2). In these two cases, most of the conceptual work was done by the human;
however, progress in data mining and machine learning (Fürnkranz & Kubat,
2001) makes it likely that, in the foreseeable future, extraction of principles
and concepts will be done automatically.
   Donkers and Uiterwijk (2002) generated 100,000 random bao games to
study the average game length and computational complexity of the game.
The computer generated a similar game length as the average found by de
Voogt (1995) in a 92-game championship with masters. Their statistics also
indicated an increase in the number of move choices in set stages of the game,
data that are nearly impossible to obtain without computer aid.
   Large databases of games can also be used to study psychological aspects
of game playing. For example, Jansen (1992, 1993) scanned chess databases
to find examples of typical mistakes in King and Queen versus King and
Rook endgames. Based on this information as well as other sources, Jansen
built a program that took advantage of humans’ propensity to use typical
heuristics, such as giving check frequently with the Queen or trying to set up
shallow threats.
   Another use of archives is to estimate the amount of knowledge required
to become a master. Charness’ (1991) approach was to get estimates of the
size of the task environment by considering the number of lines contained
in opening and endgame books. Finally, ratings can be used as data. Elo
(1978) looked at historical trends in the distribution of ratings, and Charness
(1989) analysed the rating of a master over a protracted period and suggested
that, at least in this case, the development of expertise followed a power law
of the amount of practice.
   Archives and databases offer several other opportunities still largely
unexplored. For example, there is almost no longitudinal study dealing with
the progression from novice to expert. A possible approach would be to
take advantage of amateurs’ practice, in particular in chess, of storing their
(official) games into a database. To study development toward high-level
expertise, one could retrospectively study the games of a player who has
managed to make the transition from novice to expert. The amount of
data to analyse would be important—perhaps in the order of 1000 games
(100 games a year in 10 years)—although machine-learning techniques could
be used to at least infer key patterns from these games. While such an
approach would ignore many relevant factors, such as friendly games, book
study, and interaction with a coach, it may be a good start for characterizing
expertise development.
196   Moves in mind
Observations and natural experiments
Valuable information can be gleaned by simply observing players or analysing
tournament results. An early example is offered by Rayner’s (1958a, 1958b)
study of pegity, where he simply observed children and adults engaged in a
tournament. Another example is provided by Gobet and Simon (1996d),
who used a series of simultaneous displays played by world chess champion
Gary Kasparov against national and championship teams to investigate the
respective role of pattern recognition and search in chess skill.


Interviews and questionnaires
Questionnaires have been used in three main ways. First, as a means to obtain
information about players or aspects of the game. Second, as means to
control variables that may confound the measures of interest. And third,
as measures of the dependent variables under study. To the first category
belong studies like Binet (1894) and Cleveland (1907), who used informal
questionnaires, and, more recently, Pfau and Murphy (1988), who developed
a structured questionnaire measuring chess knowledge. The second category
includes studies like Gobet and Waters (in press), who used a questionnaire to
control the amount of motivation of players of different skill levels. The third
category can be illustrated by Gobet and Retschitzki (1991), who adminis-
tered a standardized questionnaire to measure the effect of noncontrollability
on variables such as depressivity and anxiety.


Introspection and retrospection
A simple, albeit ‘soft’, method of investigating game experts’ thinking pro-
cesses is to ask them what they think, either concurrently (introspection) or
retrospectively (retrospection). (Note that introspection and retrospection
should carefully be distinguished from concurrent protocol analysis (Ericsson
& Simon, 1993), which will be discussed in the next section.) The dis-
advantages of such methods are well known: bias in reporting, tendency to
rationalize, ambiguity, to name but three. The advantages are important as
well: given their status as experts, the players probably have something
important to say; the players’ introspections may suggest new hypotheses or
research directions to the psychologists, who may themselves be victims of
biases in the way they approach the domain; and finally, as de Groot has
proposed, experts’ introspections can be used as data. That is, introspective
reports inconsistent with a theory should count as negative evidence against
that theory (e.g., de Groot & Gobet, 1996).
   The use of introspective protocols is not without practical difficulties.
Rayner (1958a, p. 159) states that: ‘Introspective reports were excluded
because the subjects were reluctant to give them repeatedly for the many
sessions they had to attend.’ Moreover, with board games, the availability of
                                      Methodology and research designs 197
verbal labels or a notational system is a general methodological problem for
introspective reports and verbal protocols. Verbal labels relating to specific
openings, positions, strategies or tactics differ greatly in number and kind
between various strategy games. So far, introspective reports have been
recorded mainly for chess and Go.


Protocol analysis
Protocol analysis consists in recording and analysing subjects’ verbal
utterances and motor actions. We consider in turn verbal protocols, eye
movements, and hand/finger movements.


Concurrent verbal reports
In research using verbal protocols, participants are not asked to theorize
about the way they think, memorize, perceive, for instance, but to think aloud
when carrying out a task. Subjects are specifically encouraged not to produce
hypotheses about their thinking processes. This method is reliable in domains
in which people naturally use a verbal mode of thinking, such as arithmetic
(Ericsson & Simon, 1993). How does it fare with board games, which pre-
sumably tap visuo-spatial modes of processing? It has given useful infor-
mation about thinking processes in chess and Go, perhaps because players
regularly use a notational system and a jargon to communicate with
colleagues. Even here, there are basic limits about what verbal protocols can
tell us about processes that occur rapidly and unconsciously, such as per-
ceptual processes. In addition, as noted earlier, the absence of a notational
system in some games hinders the use of verbal reports.


Eye movements
It is a common assumption in cognitive psychology that eye movements give
reliable information about what is heeded to, and, therefore, give clues to the
contents of thought. Hence, it is no surprise that, in order to study cognitive
processes, researchers have recorded eye movements in various tasks, such
as reading, driving, music, and game playing. With board games, almost all
research has been done with chess, as far as we know. (The exception is a brief
mention of this technique with Go in Yoshikawa & Saito, 1997a.) Even
though earlier work used rather crude eye trackers by current standards,
important insights were gained about problem solving, perception, and
memory. Recent work has used more precise eye trackers, both spatially
and temporally, which provide data that can test the fine grain of theories and
enable sophisticated experimental manipulations, such as the gaze-contingent
window paradigm (see Chapter 3).
   Eisenstadt and Kareev (1977) developed a ‘window-mode’ technique,
where the board is presented on a computer screen and a light pen reveals the
198   Moves in mind
contents of a selected square. By artificially blocking peripheral vision, this
technique allows the researchers to have a good idea of where the participants
are attending to, although with less precision than with an eye-movement
apparatus. This technique made it possible to collect simultaneously verbal
protocols and information about attention. In addition, it could be used
when participants were playing their own games.
   Eye-movement and window-mode studies are problematic in settings
where participants play illiterate games or are not computer literate. In this
case, simpler but more ecological methods are possible. The equivalent of
blocking peripheral vision can be obtained, for instance, by having holes on
the board covered by pieces of carton and uncovered by the player when
calculating or evaluating a move. When performing on bao tasks that were
complicated by the blocking procedure, players showed a significant reduc-
tion in calculating performance (de Voogt, 1995). This was taken as evidence
for the importance of repetition—that is, when players go over the holes with
counters many times, they are able to calculate more duru than if they have to
rely on memory because the holes are covered.


Hand and finger movements
In board games, strong players have the ability to look ahead in their mind’s
eye, without any overt behaviour. Weaker players, in particular novices,
sometimes supplement their internal processing capacities by moving their
hands or fingers over the board. While we are not aware of any psychological
research using this type of data with novices, such information has sometimes
been used with blind players. For example, Tikhomirov and Terekhov (1967)
studied a blind chess player, who was accustomed to touching the board
with his fingers when thinking about a move. Finger movements could be
interpreted as meaningful trajectories given the semantics of the position.
   In bao, much of the quantitative data were gathered by finger-movement
observations recorded on video (de Voogt, 1995). During the calculation of
complicated moves, the use of a finger to keep track of the calculation
progress did not seem to interfere with, and even helped, expert performance.


Standard experimental manipulations
It may be worthwhile discussing some of the experimental techniques
typically used in board-game research, in order to identify possible trends.
We start with perception, and then deal with memory and problem solving
in turn.


Perception
In addition to eye-movement tracking, discussed above, perception has been
mainly studied by detection-task techniques. For example, Saariluoma (1984)
                                      Methodology and research designs 199
asked players to detect the presence of various features (e.g., King in check),
and recorded reaction times. Other standard techniques from experimental
psychology have occasionally been used, notably in the study by Reingold
et al. (2001), who employed a variation of the Stroop task for chess (see
Chapter 4). Conversely, the manipulation of chunking in perception tasks,
which originates from chess, has also been used in other domains of expertise,
such as electronics.


Memory
Experiments in board-game research have been dominated by research on
memory, and most research on memory has been done using a free-recall
paradigm. Several of the most robust results in board-game psychology
come from this line of research. In the typical experiment, derived from
de Groot’s (1946) recall task, several independent variables have been
manipulated, including: presentation time, number of pieces, number of
boards, level of randomization or distortion of a position, presence of an
interfering task, sensory modality used, and, obviously, skill level. Some
experiments have combined several of these variables, for example,
Saariluoma (1992b) coupled a verbal presentation of the board with
interfering material.
   Given their popularity in experimental psychology, recognition experi-
ments have been surprisingly rare with board games (see Chapter 5), perhaps
because skill effects have been harder to produce with this technique. A
natural strategy would be to adapt the many manipulations done with
recognition experiments in, say, verbal memory, to board-game research. This
could also be a way to link board-game studies to mainstream experimental
psychology.


Learning
As seen in Chapter 7, there has been a continuing interest in the way novices
learn aspects of board games, at least since Rayner’s (1958a, 1958b) study on
pegity. Here, one is less interested in skill itself than in the way people
learn or deal with new complex tasks. Rayner himself used a methodology
based on observation, but there are examples of experimental studies as
well. For example, Ericsson and Harris (1990) introduced the technique of
training novices to memorize chess positions over several months. This tech-
nique has the advantage of offering high-density data, ideal for modelling.
Additional examples of learning experiments are reported in Fisk and Lloyd
(1988), who studied the decrease in reaction time with subjects learning a
simple version of chess, and N’Guessan Assandé (1992), where novices were
observed in the way they learnt awele. In most of these cases, the data were
collected by a computer, offering a powerful tool for gathering detailed
and precise data. With current technological advances, we expect that such
200   Moves in mind
computer-supported collection of data will become more prevalent in the
near future, at least in industrialized countries.


Problem solving and reasoning
Research in problem solving has been dominated by the choice-of-move
task originated by de Groot (1946). The typical dependent variables are the
quality of the chosen move, the macrostructure of search, and the solution
time. This task, which can be coupled to a recall task, incorporates both
the virtues and defaults of concurrent protocols, which we have discussed
above. It can also be used to study specific mechanisms related to problem
solving, such as evaluation (Holding, 1979). A further possibility is to
manipulate the type of positions used to elicit protocols, for example by
comparing endgames with middlegames. A nice variation of this idea was
provided by Saariluoma (1990, 1992a), who used positions likely to induce
stereotypical solutions, even though shorter solutions exist; the importance
of Saariluoma’s study is that the problem-solving task can now be used to
test specific hypotheses, and not only as a means to produce observational
data. A similar approach was used by Marmèche and Didierjean (2001), who
manipulated the type of instruction given to novices in a induction task, and
observed its effect in a problem-solving situation.
   Few data are available about players’ eye movements when they consider
the next move (see Chapter 6). In particular, eye-movement recording has
not been combined with thinking out loud, which could present convergent
evidence about players’ cognitive mechanisms.


Neuroscientific approaches
As discussed in Chapter 9, little research has so far used techniques from
neuroscience. The few studies available used various brain-imaging tech-
niques, electroencephalograms, handedness questionnaires, and post-mortem
studies of brains. While we expect brain-imaging studies to be common in the
near future, we warn the reader not to be over-optimistic about the potential
scientific gains, for three reasons. In many board games, the key ingredient to
expertise is the knowledge and experience amassed over years of practice.
Experts use more recognition memory than weaker players and brain-
imaging techniques may provide evidence as to which brain structures
encode this information. However, beyond this, these techniques are unlikely
to tell us much about experts’ knowledge. Second, decision processes leading
to the choice of a move often last several minutes; current brain-imaging
techniques are weak at recording behaviour over such long periods. Finally,
current technology is more applicable when simple tasks are used (e.g.,
discrimination between two pieces), tasks which may miss crucial aspects of
expertise.
                                      Methodology and research designs 201
Typical research designs

Cross-sectional skill comparisons
Our present knowledge of cognitive processes in game playing has largely
been gained using the so-called expert/novice paradigm, that is, by making
cross-sectional comparisons of players of different skill levels. The main
reason for this indirect approach is that longitudinal empirical research on
the acquisition of complex tasks such as board games is difficult, calling for
repeated observations over the prolonged period (at least a decade, in most
cases) that a novice takes to become an expert.
   The situation is somewhat better in games such as chess, where the presence
of a quantitative rating scale makes it possible to compare players at a finer
grain than just the contrast between experts and novices. Indeed, thanks to
the Elo rating, several investigators have avoided grouping players into
skill classes and have used statistical techniques such as regression analysis
to make sense of their results (e.g., Charness, 1981b; Gobet & Waters,
in press).
   Nevertheless, board-game research has commonly compared groups of
players of different ability. While this approach has allowed researchers to
find several, sometimes surprising skill differences, it has also been criticized
(e.g., Gruber et al., 1994). What is lacking with this approach is an indication
of the transition mechanisms that allow players to move from novice to
expert level through several intermediate levels. Longitudinal designs are
necessary for making such inferences.


Longitudinal studies
Practical considerations have discouraged the use of longitudinal studies and
instances of such designs are rare. Some of the few examples come from the
study of intelligence (e.g., Frank & d’Hondt, 1979), where, admittedly, the
focus of interest is more the relationship between intelligence and skill in a
given game than the detail of skill development. As mentioned earlier, the
acquisition of skills for limited aspects of a game was the object of several
longitudinal studies. To our knowledge, the only longitudinal study interested
in the acquisition of high levels of expertise is Charness’ (1989), who exam-
ined the same chess player twice, across a 9-year interval.
   While there are few studies documenting how a novice becomes an expert
player in complex games, there exist several studies about how novices learn
a simple game, such as tic-tac-toe or pegity (see Chapter 7). The general
accessibility of simple board games facilitates experiments with participants
familiar with the material, and their simplicity allow people unfamiliar with
them to learn them rapidly.
202   Moves in mind
Mathematical and computational modelling

Mathematical modelling
Mathematical techniques have been sometimes employed in board-game
psychology. Simon (1974) drew on a lattice representation to formalize the
concept of error in chess. Using standard probability theory and information
theory, de Groot and Gobet (1996) estimated the number of ‘master-like’
games in chess, while Simon and Gilmartin (1973) extrapolated the number
of chunks held in masters’ LTM from their computer simulations. Several
studies have attempted to estimate the number of possible positions in
various games (see Chapter 2). All of these studies led to the production of
worthwhile knowledge about the statistics of board games, and helped
develop theories of the task environment (Newell & Simon, 1972). Somewhat
surprisingly, little work has been done in board games using game theory.


Artificial intelligence and computer simulations
As seen in Chapter 2, the computational exploration of board games has
been vigorously pursued in computer science and artificial intelligence. (Some
researchers, such as Donkers & Uiterwijk, 2002, for bao, had sometimes
to adjust game rules in order to be able to program the game under study.)
A great deal has been learnt about board-game complexity and the means
to tame it by artificial methods. Another source of worthwhile information
is offered by current research in machine learning aimed at identifying
patterns and principles from databases of masters’ games. Several artificial-
intelligence researchers have developed programs based on selective search,
which contrast with brute-force approaches such as Deep Blue. As mentioned
in Chapter 6, Pitrat (1977) has written a program that uses several heuristics
to limit the search tree to the same size as humans’ (about 100 positions).
These programs could provide ideas for experiments on human selectivity in
problem solving. Overall, the resources provided by artificial intelligence have
been underused by psychologists.
   The goal of computer simulations in psychology is to reproduce the detail
of the cognitive mechanisms and knowledge structures engaged in a given
task. As seen in several chapters of this book, simulation of board-game
behaviour has been dominated by Herbert Simon and his colleagues, who
have modelled aspects of perception, memory and problem solving in chess
for almost 50 years. Recently, researchers have used neural networks to model
memory. It would be beneficial, both for modelling methodology and board-
game research, to compare results obtained with Simon’s approach to those
obtained with neural networks.
   Advantages of computational modelling include theoretical precision,
ability to make quantitative predictions that can be then tested by experi-
ments (e.g., Gobet & Waters, in press), and provision of mechanisms
                                       Methodology and research designs 203
explaining how intelligent systems can make use of the information con-
tained in their environment (in the case of board games, games played by
masters and grandmasters). Unfortunately, these benefits do not come with-
out costs, which may explain why relatively few researchers have opted for
computer modelling in addition to empirical work. Even with substantial
progress in high-level programming languages, the development of a model
and its testing with empirical data is a slow process.


Weaknesses and strengths of methodologies used in
board-game research
In order to provide guidance to further research, we identify the weaknesses
and strengths of the kind of research typically carried out for studying board-
game psychology. We start with the weaknesses, and consider the strengths
next.


Weaknesses
One obvious weakness, when compared to other experimental work in
psychology, is the small sample size often used in board-game research. This
shortcoming is actually typical for expertise research, where experts are few
by definition. Small samples raise the issue of statistical power, that is, the
ability of an experiment to statistically detect genuine group differences.
A telling example of this difficulty is the research into the recall of random
positions. For a long time, it had been believed that there was no skill effect in
the recall of briefly presented random positions, as opposed to the recall of
game positions, where a strong skill effect was present (Chapter 5). Recent
research, using both meta-analysis of available studies and new experiments
with larger samples, has shown that stronger players do reliably recall
more than novices from random positions, even though the effect is small.
This result, theoretically important for evaluating theories of expertise
(Gobet, 1998b; Simon & Gobet, 2000; Vicente & Wang, 1998), faced the
danger of being overlooked due to poor statistical power. In general, the
strategy of using small samples, even single subjects, which can be found
in many classical studies of board-game research (e.g., Chase & Simon,
1973a; de Groot, 1946; Reitman, 1976), works fine when clear differences
are encountered. However, it is not appropriate for asserting the lack of
differences between players of different skill levels.
   Another weakness is that studies have rarely been replicated or extended to
other board games or other domains of expertise (Charness, 1992; Gobet,
1993b). As with the issue of sample size, this is readily explained by the
difficulty of finding experts. But, precisely because of limited sample sizes,
the need of replication is evident, in particular with experiments that failed to
identify skill differences. This lack of replication has significant consequences
for the generalizability of results.
204   Moves in mind
Strengths
Given the joint weaknesses of sample size and lack of replication, the strong
impact of board games in psychology may appear paradoxical. An analysis
of the strengths of this type of research holds the answer to this conundrum.
First, board-game research has a strong ecological validity. This contrasts
with most of psychology research, based on a student population. Players
spend many hours—tens of thousands for professionals—practising their art,
which ensures that they are highly familiar with the domain. They also tend
to be motivated to perform well, despite the sometimes convoluted nature
of the experimental task. Second, most games have a reliable rating system.
In some cases, like chess, the measurement system is mathematically sound
and offers quantitative measures.
   Third, experts can be found in domains which can be controlled for a large
number of contextual factors including age, gender, nationality, education, or
‘culture’ in the broadest sense of the word. Fourth, the experimental effects,
when they are present, tend to be strong. This is because the comparison
often includes the extremes of experts and novices. For example, the dif-
ference in recall between chess grandmasters and amateurs is so large for
game positions that no sophisticated statistical technique is necessary to
uncover it. Finally, board-game phenomena have been shown to generalize
to other domains of expertise and to cognitive psychology in general.
11 Conclusion




Board-game complexity
A common theme has run through the chapters of this book. How can intel-
ligent systems master complex environments such as bao, chess or Go, where
a combinatorial explosion typically forbids exhaustive search? A first answer
was offered by our review of the state of the art in computer board-game
playing. There, we saw that simple board games can be solved by exhaustive
enumeration of all positions, while complex games such as Go still challenge
technology and artificial intelligence. With several games of medium com-
plexity, such as checkers or chess, computers’ success rely on a combination of
brute search, selective search, efficient evaluation functions, and substantial
knowledge bases covering openings and endgames. An unexpected outcome
of this rapid progress is that computers can now be used to explore aspects of
human cognition.
   Still, humans perform remarkably well, if one takes into account the extent
of their cognitive limitations—including limitations in memory capacity,
learning rate, and speed at which they can evaluate states in a problem space.
Human thinking processes, which are clearly different from computers’,
provide a second approach of tackling the complexity problem. As was dis-
cussed at length in this book, human experts rely on pattern recognition
and selective search—in essence what was proposed by Simon’s (1947, 1955)
theory of bounded rationality.
   In the last decades, board games have offered psychologists a unique win-
dow on human cognition and its limits, as can be seen by the rich set of
empirical data collected and the number of computational models developed
for simulating aspects of perception, learning, memory, and problem solving.
A number of key ideas in the study of human cognition have been formulated
and refined within the realm of board games. These ideas include selective
search, progressive deepening, and the role of perception and knowledge in
problem solving. The core ideas are now supplemented by data on develop-
ment and ageing, and on how knowledge is transmitted through education.
To a lesser extent, these ideas are also being extended by empirical evidence
showing how cognition relates to talent and intelligence, how it is mediated by
206   Moves in mind
emotions and motivations, and how it is implemented in the brain. The
board-game microcosm can thus be seen as a reflection of research in
cognitive psychology in general.


Landscape of board games
The rich material we have described in this book does not hide a clear imbal-
ance in the attention given to the different board games. Chess has dominated
research, while some games, most notably checkers, draughts, and back-
gammon, are almost absent in spite of their widespread popularity. There
is no doubt that these games present a rich source of experimental and
theoretical material that has yet to be explored. At least two avenues are open
for research in these games. One can either attempt to replicate research
conducted with other games and further test standard theories in the
field. Or, perhaps more interestingly, one can devise new experiments that
capitalize on features specific to a given game or take advantage of its
environment.


Impact of board-game research
Psychologists using board games are interested in understanding general
principles of cognition, and empirical work on board games has had a
respectable impact on psychology at large, with some works by researchers
such as de Groot (1946) and Chase and Simon (1973a) being considered
classics in the field. Given the amount of empirical work done on board
games, it is not surprising that this area of research has generated several
detailed theories, some of them implemented as computer programs. These
theories—notably Chase and Simon’s chunking theory—have influenced
cognitive psychology (Charness, 1992). Even now, the chunking theory
accounts for the data on expertise better than several alternative theories
(Gobet, 1998b). While perhaps most evident for the subfield of expertise
research, this impact is also apparent in the psychology of perception,
memory, and problem solving.
   This research has also had clear impact on our knowledge of board games.
For example, de Groot and Jongman’s (1966; Jongman, 1968) work has
assisted the mapping of the complexity landscape of chess. Others, such
as Retschitzki (1990) and de Voogt (1995), had to provide details about
rules, players, history, and environment before presenting their experimental
psychological results.
   The contribution of artificial-intelligence research to psychology has
been reciprocated. Artificial intelligence has taken concepts such as selective
search and pattern recognition to implement its models and theories. At the
same time, artificial-intelligence research has given much attention to board
games other than chess that have been otherwise ignored in cognitive
psychology.
                                                              Conclusion    207
Future
Among the many questions mentioned in this book, several are likely to
generate vigorous research in the near future. In particular, three lines may be
highlighted here: an empirical, a theoretical, and an applied line. On the
empirical side, it is probable that the current enthusiasm about neuroscience
will lead to further data collection on the biological underpinning of board-
game playing, in particular with brain-imaging techniques. We also expect
that creativity and implicit learning in board games, two themes rather
ignored so far, are likely to capture researchers’ attention.
   On the theoretical side, we expect Newell’s (1973) call to be followed: a
computational theory of human game playing will be developed that largely
accounts for human behaviour when playing a given game (Newell had chess
in mind), or, even better, across several games in different cultural contexts.
Two recent developments have made reasonable progress in this direction.
The CHREST/SEARCH family of programs simulates human behaviour
closely, but in only one board game (chess). By contrast, HOYLE shows
generality by learning to play a variety of (simple) board games, but it has not
yet been compared in detail to human data.
   Finally, we anticipate more research into education and training tech-
niques, where a combination of psychological theory and empirical field
work can further the development of real-world applications. In other words,
we have moves in mind, which we explore, try to understand and finally put
on record both as players and as psychologists.
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Appendix 1
Rules of board games




For the purpose of future research the rules of board games used in
psychology should be explained. It appears that only the board, the pieces,
and the elementary rules of movement (including capturing) are essential. It
is these basic rules that have been presumed understood in research or have
been briefly explained to make sense of an experiment. The detailed rules
of chess and shogi will not add to a better understanding of the experi-
ments conducted with these games; similarly, the variations of gomoku and
mancala are only of limited interest for psychologists or readers of this book.
   Classifications of board games have concentrated on the strategic purpose,
and types of movement in a game. A complete description of complex board
games may include rules that rarely occur or rules that may vary among
players groups. A limited but consistent description (see Table A1.1) allows
the reader to take note of most board games presented here and compare
their characteristics and use for their own research purposes. In some cases,
the rules of the game need little explanation beyond what is listed in the
table. The following references provide a complete description of game rules,
variations on existing rules as well as the areas in which particular board
games are played; for awele: Retschitzki (1990); for bao: de Voogt (1995); for
mancala games in general: Deledicq and Popova (1977); for chess: Hooper
and Whyld (1996), Murray (1913); for board games in general: Murray (1952),
Bell (1960), and Parlett (1999).


Purpose of the game
The classification of board games by Murray (1952) and others has been
largely based on the purpose of the game. War games require captures and in
race games the players race each other to reach the end of the board. While
war games have been particularly useful in psychology, race games have
received little attention. Backgammon is one of few race games in which
strategy plays an important role. Monopoly is a race game but with a theme.
Although captures are possible in backgammon, the purpose of (most)
backgammon variations is not to capture the majority of pieces. Captures are
simply a means to an end.
Table A1.1 Characteristics of selected board games

Game name           Purpose of the game Move characteristics Piece characteristics      Number of fields   Number of pieces

Awari, awele        Capture most            Distribute pieces    Equal value and        12, circular      48
                                                                 same colour
Backgammon          First to reach the      Moves forward        Equal value and two    24, line          30
                    other side              according to dice    colours
Bao                 Capture most            Distribute pieces    Equal value and        32, circular      64
                                                                 same colour
Chess               Capture King         Moves different per      Different value and     64                32
                                         piece                   two colours
Checkers,           Capture all          Moves equal except      Equal value and two    64, 100           24, 40
draughts                                 promoted piece          colours
Fox and geese       Capture all or block Moves different per      Different value per     25                12 one side,
(simplest           all                  side                    side and two colours                     1 other side
version)
Go                  Capture most            Place on any empty   Equal value and two    361               361
                                            field                 colours
Gomoku,          First to make five in Place on any empty     Equal value and two   225                225
pegity           a row                field                   colours
Kalah            Capture most         Distribute pieces      Equal value and       12 + 2, circular   48
                                                             same colour
Mastermind       Guess in fewest tries Place on section of   Different value        44                 44
                                       empty fields
Monopoly         First to reach        Moves forward         Equal value and       40, circular       2–4
                 fortune               according to dice     different colour
Nim              Block all             Start at any empty    Equal value and two   Varies             Varies
                                       field                  colours
Othello          Capture most          Place on any empty    Equal value and two   64                 64
                                       field                  colours
Shogi or         Capture King          Moves different per    Different value and    81                 40
Japanese chess                         piece                 two colours
Sungka, dakon    Capture most          Distribute pieces     Equal value and       12–20, circular    72–200
                                                             same colour
Tic-tac-toe      First to make three   Place on any empty    Equal value and two   9                  9
                 in a row              field                  colours
240     Appendix 1: Rules of board games
   Alongside the war and race games, there are the alinement games
which require players to line up their pieces in a row of a certain length. The
rules of these games are in general simple, but gomoku is known to have
intricate variations in which, for instance, it is not allowed to make six-in-a-
row. These variations have limited purpose in psychological experiments in
which the game was used. Frequently, even the experimenters fail to mention
the particulars of the variation they have used.


Move characteristics
As much as its purpose, the way of moving characterizes a board game. The
board games classified as war games appear to have distinct ways in which
their purpose of destroying the opponent is achieved. In cognitive psychology
these distinctions have played an important role.
  There are three principally different ways of using pieces. In chess, shogi,
and checkers, one or two pieces at most move across the board and this also
applies to the race games. In mancala games such as awele, and bao, one
distributes a number of pieces at the same time. In Go, Othello, and gomoku,
one places a piece on the board rather than moving it across the board.
Othello is an exception since, in this game, one piece is placed on the board
but a number of other pieces may change colour. This creates a volatility of
position that is otherwise only found in mancala games.


Number of fields and pieces
In board games, the pieces move on a board that defines the spatial
boundaries. In the majority of the games the pieces are divided in two
colours, each colour for one of the two players. Most board games used
in psychology are two-person games. In mancala games, the pieces change
ownership and therefore have no distinct colours. While in most games pre-
sented here each piece has the same value, in chess there are six values and
certain chess variations have even more. The differences in the type of pieces
are also reflected in the moves and strategies.


Description of selected board games

Awele
Awele is a mancala game. It is also known as awari, oware, or, simply,
mancala. There are a number of awele variations, which are not relevant for
the research results discussed in this book. Awele consists of two rows of six
holes and 48 pieces, commonly known as seeds. Each player owns one row.
The purpose of the game is to capture the majority of the seeds.
  A move consists in picking up the contents of one hole, and distributing
the seeds one by one in consecutive holes counterclockwise. Once the last
                                           Appendix 1: Rules of board games   241
seed is spread the move ends (see Figure A1.1). If the last seeds enters a hole
on the opponent’s row making a total of two or three then these seeds are
captured and taken from the board. If the holes on the opponent’s row
directly preceding this capture also contain two or three seeds, these may also
be taken as long as there is an uninterrupted row of twos and threes. When a
hole is played with more than 11 counters, making a complete round of the
board, the player omits the starting hole when spreading its contents.




Figure A1.1 Examples of awele positions.
242   Appendix 1: Rules of board games
   If a player has no more seeds to play, the game ends and the captures are
counted to determine the winner. Most awele variations refer to rules that
require a player to play seeds into the opponent’s row when the opponent has
no seeds left. Although these rules are essential in a game, and have strategic
relevance, the details of these rules are usually not relevant to psychological
inquiry.


Bao
Bao, which is also a mancala game, consists of four rows of eight holes
and 64 pieces, commonly known as seeds. Each player owns two rows. The
purpose of the game is to empty the inner/front row of the opponent.
  A move consists in picking up the contents of a hole and distributing
the seeds one by one in consecutive holes in clockwise or counterclockwise
direction in one’s own rows. If the last seed in hand enters into a hole already
containing seeds, this seed, together with the contents of that hole, is taken
up. The move now continues in the same direction until the last seed of a
spreading enters an empty hole, which constitutes the end of the move. This
principle of ‘relay laps’ creates a series of changes on the board. If the move
makes several laps around the board then players will eventually find it
impossible to calculate the end of the move beforehand.
  Captures are made when a hole on the inner row is reached that has seeds,
while the opposite hole of the opponent also contains seeds. The opponent’s
seeds are then taken, and spread into the inner row of the player who cap-
tures, thereby continuing the move. This principle of capturing continues the
changes on the board. The rules for capturing are notoriously complex, and
involve direction changes as well. Experiments with this game have largely
been limited to the simple relay lap without capturing, measuring the number
of position changes that experts could calculate.


Checkers and draughts
Checkers is a war game played on a checkered board with two sets of
identical pieces. One set is white or red while the other is black. The players
play only on the squares of one colour. At the beginning of the game,
pieces of each player are placed on their side of the board, leaving two
rows open in the middle between the two players. A move typically consists
in moving one piece diagonally across the board reaching an empty square
of the same colour. Captures are made if an opponent checker is in the way,
with an empty square in the same diagonal line directly behind it. In this
situation, the player may jump over the opponent’s piece and remove it from
the board.
   The number of squares on the board, the colour and number of the pieces,
the colour of the squares used for play, the position of the board between the
players as well as the possibility of moving backward, making multiple
                                       Appendix 1: Rules of board games 243
capture or jumping more than one empty square differ between regions.
In all variations, the purpose of the game is to capture all the pieces of the
opponent. If only the majority of the pieces can be captured, the game
is considered a draw. Since the game is known as a children’s game in
some countries, notably Germany and the United States, this has resulted
in little research on expertise even though competition is strong in other
countries, particularly where so-called international draughts is being played
on a 10 × 10 board, notably in Russia, the Netherlands and large parts of
West Africa.


Chess, shogi, and shiang qi
International chess is played on an 8 × 8 board. The object of the game is to
capture (checkmate) the opponent’s King. Each side, called white and black,
has eight pieces and eight Pawns. At the start of the game, the white pieces are
placed on the first row in this order: Rook, Knight, Bishop, Queen, King,
Bishop, Knight, and Rook. The eight white Pawns are placed on the second
row. A similar arrangement is used for black on the eighth and seventh
rows. Rooks move in straight line, horizontally and vertically, and Bishops in
diagonal. The Queen combines the movements of the Rook and the Bishop.
The King moves one square in any direction. The Knight moves first one
square horizontally and vertically, and then one square ahead diagonally. It is
the only piece than can jump over its own pieces. With all pieces, when a move
ends on a square occupied by an opponent’s piece, this piece is captured.
Pawns move one square forward (from their starting square, they can also
move two squares forward), and capture one square in diagonal. Special
rules include castling (where both the King and a Rook can move), taking
enpassant (where a Pawn moving two squares from its starting location can
be taken as if it had moved only one square), and stalemate (a draw condition
where one side cannot move but is not in check).
   The differences between international chess, Japanese chess (shogi), and
Chinese chess (shiang qi) are significant, but have not been part of psycho-
logical investigation. Since international chess and Chinese chess are played
at a high level in China, such a study could reveal the psychological impact
of these differences. The first difference is that the board in Chinese chess is
not a set of squares but a set of intersections which are not connected like
squares. Instead, there are areas in which the movement of pieces is con-
strained by the design of the board (see Figure A1.2). In addition, certain
piece movements are unknown in international chess. The return of captured
pieces on the board at the will of the player, as is common in shogi, is not
possible in international chess. Again, these differences in rules have not been
the subject of psychological investigation, despite the apparent availability of
the game and its experts.
244   Appendix 1: Rules of board games




Figure A1.2 Initial position in shogi.

Fox and geese
Murray (1952) describes several hunt games similar to fox and geese; in the
variant studied by Gottret (1996), one player has 12 geese and the other a fox.
Players move alternately and both fox and geese can move along a line to
an adjacent point. If the fox jumps over a goose, the goose is killed and
removed from the board. The geese cannot jump over the fox but instead try
to crowd him into a corner, making movement impossible. The fox wins if
he can deplete the geese so that they cannot trap him. If the geese are played
correctly they should always win.


Go
Go is a war game. All white and black pieces are of the same kind and the
players place them alternatively on the board. The object of the game is to
enclose the pieces of the opponent, which equals a capture. Go is played on a
19 × 19 board, but psychologists have often used smaller boards to limit the
number of potential moves.
                                      Appendix 1: Rules of board games     245
Gomoku, pegity, and three-in-a-row/tic-tac-toe
Gomoku is a Japanese variation of an older game that also existed under the
name of pegity in the United States. Each player owns pieces of one colour
and places one piece per turn onto the 19×19 board. The first to have five
pieces horizontally, vertically, or diagonally adjacent on the board wins the
game. There are variations of the game which mainly limit the first moves
allowed on the board. This is in order to equalize the chances of each player.
Some variations do not allow six-in-a-row as a win.
   Tic-tac-toe is played on a 3×3 board with each player owning usually
crosses or noughts. The first to make three-in-a-row wins. This game has been
used mostly in developmental studies where the simplicity rather than the
complexity of a game was essential.


Mastermind
Mastermind is a guessing game and has not always been considered a board
game. Parlett (1999) in his history of board games, for instance, does not
mention it. The game could just as well be played with cards, which would
make this game, just like dominoes, a card game. Unlike bridge, dominoes
and mahjong, the game is not part of the card-game research tradition.
Obviously, this does not mean that its research potential should not be taken
seriously.
   Mastermind is played on a peg board with 11 rows of four holes. The first
row, behind a small screen, hides a ‘code’ generated by one player. This
code consists of six different colours of pegs placed in some sequence.
Each attempt by the second player to guess one of the 1296 possible codes is
represented by one of the 10 remaining rows. Once the guessing player has
placed an attempt on a row, the player owning the code row gives two types
of feedback: the number of pegs with both correct colour and location, as
well as the number of pegs with correct colours but wrong location. The
object of the game is to find the code as rapidly as possible, but within 10
trials. Simplified versions with fewer distinguishing colours are also possible.


Nim
Nim is a category of games in which each of two players in turn places (or
moves) a piece on the board in such a way as to restrict the subsequent power
of placement (or movement) of the other player. The first player unable to
continue loses (Parlett, 1999, p. 159).


Othello
Othello is a war game which is played on an 8×8 board. Each player owns a
set of pieces that are white on one side and black on the other. A player uses
246   Appendix 1: Rules of board games
one side of the piece, either white or black, when placing a piece on the board.
At the beginning of the game, the centre of the board contains two white and
two black pieces placed diagonally. The object of the game is to have the
majority of the pieces on the board showing one’s colour.
  Each player alternatively places a piece with their colour up, with the
requirement that a move ‘flips’ at least one piece already placed on the board.
A black piece, for instance, is always placed next to a white piece in such a
way that one or more white pieces are now in between two black pieces. This
mandatory move changes all the white pieces to black by turning the white
pieces around. In other words, each player places a piece in such a way that
enclosed pieces, horizontally, vertically, and/or diagonally, change colour to
their advantage.
Appendix 2
Measures of expertise in
board games




The notion of expertise is natural in board games. The goal of a game is to
win, and experts are individuals who tend to win (or at least not to lose) more
often than others. In addition to titles (e.g., grandmaster, master), some
games have a sophisticated way of measuring the level of expertise in com-
petition. Chess, checkers, and Othello use the Elo rating (Elo, 1978), which
updates the rating of a player as a function of the result and the strength of
the opponent. Go uses a system of 48 levels of expertise, ranging from low-
level beginner to top-level expert (Masunaga & Horn, 2000). The levels are
given by assessment, the content of which is provided by the Japanese Go
association in cooperation with other national Go organizations. Within Go,
‘kyu’ ratings, which range from 30 kyu (lowest level) to 1 kyu (highest level),
rank beginners. Above the first kyu one finds the level of amateurs, which
include 8 dan levels (from 1 dan, recognized amateurs competitors, up to
8 dan, advanced amateurs). Finally, above the amateur level, one finds the
professional level (from 1 dan to 9 dan). From a research point of view, one
disadvantage of this system, compared with the Elo rating, is that the level is
not updated after each game and that one cannot be ‘demoted’ to a lower
level.
   Several board games do not have a formal system to measure expertise.
In this case, researchers can use a variety of methods to estimate the skill
level of the players, such as consensus between players and the organization
of tournaments. The definition of ‘expertise’ is discussed in Chapter 10,
devoted to methodological aspects of board game research.
Appendix 3
Example of protocol analysis
(reprinted from Gobet, 1998a)




Position ‘A’ of de Groot (1965). Protocol of S21; age 24;
level: Expert, with an Elo rating of 2001
(Translated from French; square brackets indicate information added to the
protocol.)
  Figure A3.1 shows position ‘A’ of de Groot (1965).




Figure A3.1 Position ‘A’ of de Groot (1965).

   First phase. OK. There is an isolated Pawn for white, but it should not be
bad, because it’s a middlegame position, and it looks rather dynamic,
and one can build on it, given that there is a Knight on e5, and one can . . .
It’s advantageous. Therefore, one should try not to trade pieces off but to
bring an attack on the King’s side. Mmm . . . The black Bishop is badly
placed. Well, the first move that comes to my mind, it’s Knight e4. Yes, but
it’s dangerous because there is the Bishop on c6. I will have to check this
later. Take advantage of black’s diagonal. Maybe try to exchange the Knight
250   Appendix 3: Example of protocol analysis
on f6 to place the Knight on e4, with gain of tempo, and then, after, to have
the outpost on c5. It seems ridiculous to me, because I give up the black
Bishop. [2’]
    Episode 1. Bishop takes f6, Bishop takes f6, Knight e4, Bishop g7 or Bishop
e7. After, I cannot progress much. He is holding all the black squares.
[2’26’’]
    Episode 2. What wouldn’t be bad either is to overprotect the Knight on e5,
with a little move like Rook ‘f ’ to e1, and to see what he is doing. [2’59”]
    Episode 3. Or Rook ‘f ’ to d1. It overprotects my Pawn, which is weak but at
the same time dynamic. I’ll see. [3’30’’]
    Episode 4. Bishop h6 doesn’t look good. [3’36’’]
    Episode 5. Knight takes d5. If Bishop takes d5, Bishop takes d5, Knight
takes d5, Knight g4 . . . One takes advantage of these squares. Ahhh, but he
can take with the Pawn; it isolates the central Pawn for both of us, and then
. . . One does not have much. Ah, maybe the Pawn is on a white square and
. . . [4’24’’]
    Episode 6. Ah, maybe Pawn b4, eh? It reinforces the advance of the Pawn
b5. And then to play on the Queen’s side, by trying to bring something on c5
. . . Mmm, mmm. Especially as it is attacked, moreover, this Pawn, I see now.
[6’38’’]
    Episode 7. I can defend it by Knight c4. No . . . One takes the Knight away
from its good position, which bothers me. [7’12’’]
    Episode 8. Knight takes d5 . . . [7’25’’]
    Episode 9. Ahh . . . it can be dangerous, if he takes it . . . It can be
dangerous if he takes the Pawn b2 . . . [Irrelevant question to experimenter.]
No it’s not dangerous. [8’08’’]
    Episode 10. What wouldn’t be bad, that’s Queen d2. It controls the black
squares, and also it allows, maybe, to exchange on d5, followed by [an
exchange on] f6, and to be immediately on the black squares of the King’s
side. Then Queen d2 with the threat Knight takes d5. Either Knight takes d5,
Bishop takes e7, Knight takes e7 and Knight g4, with the threat Queen h6
and Knight f6 . . . It creates holes . . . Or perhaps? Knight takes d5, Pawn
takes d5, Queen f4, I’m attacking. He, he defends. Bishop d7. He is losing the
Pawn d5. [10’10”]
    Episode 11. Queen d2, again. Queen d2, Rook ‘f ’ to d8, Knight takes d5,
Bishop takes d5, Bishop takes d5, Knight takes d5, Bishop takes e7, Knight
takes e7, Knight g4. Ooooh . . . it gives play on the Queen’s side for Black.
[11’20”]
    Episode 12. I, I believe that one has to build up, one has to play [Pawn] b4,
and after, Rook ‘f ’ to e1, and after try to play on the black squares of the
Queen’s side. I do not see any tactical move. Ahh . . . Ahh . . . But on [Pawn]
b4, he does Knight takes c3, Rook takes c3. After, he has the outpost on d5,
with Bishop d5, or Knight d5. Let’s say Bishop d5. Then, I play Bishop takes
d5, Knight takes d5, Bishop takes e7, Knight takes e7, Rook ‘f ’ on c1, and
afterwards I have the ‘c’ column, but one gets into an endgame, and I have the
                                Appendix 3: Example of protocol analysis        251
isolated Pawn. One has to be careful. Ah . . . that’s not an endgame, with two
Rooks and one Queen, one shouldn’t exaggerate. [12’55”]
   Well, I play Pawn b4. [13’]


Extraction of the descriptive variables
The problem-solving behaviour graph of this player is shown in Figure A3.2.
The chosen move (Pb4) gets a value of 1 (out of 5). There were 12 episodes
in the protocol, the total time was 13 minutes, and the duration of the first
phase was 2 minutes. The total number of nodes is 52, and the rate of generat-
ing nodes per minute is 4 (52/13). The maximal depth is 9 (episode 11 and 12;
‘no moves’ are not counted). Taking the longest line within an episode, the
sum of depths over the 12 episodes is 44, and the mean depth is 3.66 (46/12).
The number of (different) base moves is 8 (again, the ‘no move’ is not
counted), and the rate of generating base moves is 0.69 (9/13). For the vari-
ables related to the number of reinvestigations, it helps to write down the first
move of each episode:

B × f6 Rfe1 Rfd1 Bh6 N × d5 Pb4 Nc4 N × d5 Ø Qd2 Qd2 Pb4 (Pb4)




Figure A3.2 Problem-solving behaviour graph of S21. Time proceeds from left to right
            and then down. The following evaluations are used at the end of each
            episode: + for positive, – for negative, and ? for unknown. Ø means ‘no
            move’. (See Figure A3.1 for an illustration of the chess co-ordinate
            system.)
252   Appendix 3: Example of protocol analysis
   We see that the moves Pb4 and N × d5 were both reinvestigated once
nonimmediately, and the move Qd2 was reinvestigated once immediately. We
get then a total of 2 nonimmediate reinvestigations, 1 immediate reinvesti-
gation, and 3 as total number of reinvestigations. The maximal number of
(re)investigations, both immediate and nonimmediate, was 2.
Author index




Adamopoulos, J. 108                         Binet, A. 1, 6, 31, 33–4, 65, 82, 91–3, 95,
Adesman, P. 61, 77, 87, 95                    103, 126, 196
Albert, M. L. 175, 180, 182–3               Biolsi, K. 46
Allard, F. 69                               Bloom, B. S. 156, 168
Allis, L. V. 1, 21, 26                      Bock-Raming, A. 5
Altaribba, J. 49                            Bönsch, E. 166
Alway, D. 184                               Boorman, S. A. 5
Ambrose, A. F. 150                          Booth, A. 178
Amidzic, O. 184–6                           Boud, D. 166
Amorosa, L. F. 9                            Bradley, A. C. 90, 97
Anastasi, A. 174                            Bramer, M. A. 18
Anderson, E. 90, 97                         Brannock, J. 173
Anderson, J. R. 45, 48, 137, 155, 166       Bratina, T. A. 163
Anderson, J. W. 178                         Bratko, I. 18
Antonelli, M. 184                           Britton, B. K. 97
Atherton, M. 185                            Brooks, R. L. 90
Atkin, L. R. 113                            Brown, P. 172
Atlas, R. S. 46, 67, 77–8, 96, 101–2, 119   Brügmann, B. 23
Avni, A. 178                                Brülhart, M.-L. 177
                                            Brunswik, E. 48, 190
Bachman, T. 94                              Bryant, M. 14, 21, 28
Baddeley, A. D. 90, 93, 97, 166             Bryden, M. P. 183
Bal, H. E. 21                               Buhss, U. 184
Barenfeld, M. 54, 66, 118                   Buist, S. 164
Barker, D. R. 90, 97                        Bukstel, L. 60
Barry, H. 150                               Burmeister, J. M. 18–20, 82–3, 164
Bart, W. M. 185                             Buro, M. 14, 28
Batchelder, W. H. 188                       Buschke, H. 150
Baxter, J. 22                               Bushke, A. 92
Baylor, G. W. 39, 118, 124
Béart, C. 151–2, 177                        Cage, C. E. 163
Bell, R. C. 5, 237                          Calderwood, R. 109
Berger, R. C. 46, 67, 77–8, 96, 101–2,      Campbell, M. 14, 18, 28, 149
  119                                       Campitelli, G. 93, 101, 136, 157–8,
Berliner, H. J. 14, 17–18                     160–62, 168, 172, 178, 183, 185
Berry, J. W. 49                             Carlton, P. L. 9
Bershad, N. J. 188                          Carmel, D. 24
Best, J. B. 108                             Carton, J. C. 184
Billman, D. 84–5, 194                       Cascio, W. F. 150
254    Author index
Case, R. 144                                   de la Cruz, R. 163
Cauzinille-Marmèche, E. 123, 143–4             de Saussure, F. 6
Cazevane, T. 23                                de Voogt, A. J. 2, 5, 9, 26, 32, 48, 63, 71,
Cerella, J. 149                                  77–8, 83–4, 86, 94–5, 99–100, 107–8,
Chabris, C. F. 122–3, 183, 186                   116, 136, 177, 190, 193, 195, 198, 206,
Charness, N 7–8, 41, 47, 49, 54, 56–8, 61,       237
  69, 73, 77, 87, 90, 94, 97, 101, 106, 112,   Deering, S. L. 163
  118–19, 121, 126, 129, 135–6, 138,           Deledicq, A. 163, 237
  149–50, 152, 156, 168, 171–2, 181, 195,      Dempster, F. N. 144
  201, 203, 206                                Derby, C. A. 150
Chase, W. G. 7–8, 26, 32–3, 39–43, 45, 49,     Deshayes, P. 6
  59–65, 69–70, 72–3, 75–9, 81–3, 86, 88,      Dettmar, P. 184
  93, 98–9, 101, 119–20, 122–3, 128,           DeVries, R. 142
  135–6, 156, 171, 203, 206                    Dextreit, J. 5, 8, 92, 157, 164, 167, 181
Chen, X. C. 185                                d’Hondt, W. 157–8, 161, 173–4, 176, 201
Cheng, P. C. H. 102                            Didierjean, A. 123, 200
Cherif, A. A. 8                                Diop, A. M. 152
Chernev, I. 9                                  Djakow, I. N. 31, 35–6, 70, 173, 175
Chi, M. T. H. 2, 46, 61–3, 144–5, 148          Doll, J. 174–5
Christiaen, J. 145, 148, 158–9, 161            Dollekamp, B. 164
Christie, J. F. 155                            Donkers, H. H. L. M. 21, 24, 108, 196,
Church, K. W. 17                                 202
Church, R. M. 17                               Donninger, C. 119
Clarke, M. R. B. 20                            Draper, N. R. 150
Clarkson, G. 65, 70                            Dreyfus, H. 25, 47
Cleveland, A. A. 31, 34–5, 103, 112, 127,      Dreyfus, S. 47
  148, 178, 196
Cole, M. 7, 48, 117, 176–7, 192                Eagle, V. A. 5
Cole, S. R. 48                                 Ebeling, C. 18
Cooke, N. J. 46, 67, 77–8, 96, 101–2, 119      Egan, D. E. 69
Corbett, A. T. 166                             Eifermann, R. R. 138
Craik, F. I. M. 95, 103                        Eisenstadt, M. 56, 58, 63–4, 70–71, 78,
Cranberg, L. 175, 180, 182–3                     84, 89, 116, 197
Crandall, B. W. 109                            Elbert, T. 184–6
Croker, S. 102                                 Ellis, S. H. 59, 175
Cronbach, L. J. 158                            Elo, A. E. 150, 188, 195
Crowley, K. 142, 152                           Engel, N. 5, 8, 92, 157, 164, 167, 181
Culberson, J. 28                               Engle, R. W. 69
Culin, S. 5                                    Enzenberger, M. 23
Curatola, L. 184                               Epstein, S. L. 23, 29–30
                                               Ericsson, K. A. 2, 33, 45–6, 49–50, 93,
Dabbs, J. M. 178                                 95, 98, 103–4, 122, 134–6, 156, 167,
Dalecky, A. 8                                    171–2, 187, 191, 196–7, 199
Dami, C. 143
Dan, X. 182                                    Faber, M. 5
Dankel, II, D. D. 24                           Falkener, E. 5
Darley, J. M. 180                              Farr, M. J. 2
Davidson, J. W. 136                            Fearnyhough, C. 90, 97
de Groot, A. 1, 7, 26, 29, 31, 34, 36–8,       Fehr, T. 184–6
  41–4, 48–9, 51–6, 59–62, 65–6, 69–71,        Feigenbaum, E. A. 40, 102
  76–7, 80–83, 94–5, 105–6, 108–12,            Fein, G. G. 7, 139
  114, 118–20, 124–5, 128–9, 145, 156,         Felleti, G. 166
  162, 165, 167, 177, 179, 189, 191,           Ferguson, Jr, R. 157, 160
  193–4, 196, 200, 202–3, 206, 249             Fernie, D. 142
                                                                    Author index    255
Fick, C. S. 178                              Guildford, J. P. 175
Fine, R. 8, 92, 112, 150, 181                Gut, U. 177
Finkel, I. 5
Finkelstein, L. 22                           Hall, C. B. 150
Fischer, R. J. 166                           Hamilton, S. E. 183, 186
Fisk, A., W. 57, 133–4, 199                  Hammond, K. 22
Flavell, J. H. 47–8, 145                     Harris, M. S. 134, 199
Fleming, J. H. 8, 180                        Hartston, W. R. 9, 97, 179, 181
Flinter, S. 22                               Hatta, T. 183
Fox, S. 178                                  Hayashi, H. 182
Frank, A. 157–8, 161, 173–4, 176, 201        Hayes, J. R. 115
Freud, S. 33                                 He, S. 185
Freudenthal, D. 102                          Hearst, E. S. 122–3, 167
Frey, P. W. 61, 63, 71, 73, 77, 83, 87, 95   Heller, D. 52
Freyhoff, H. 61, 64, 96                       Henson, R. 90, 97
Fried, S. 161                                Hitch, G. J. 90, 93
Frydman, M. 173–4                            Hoane, A. J. 14, 28
Fulgente, T. 184                             Hoffmann, H. 141
Fürnkranz, J. 1, 21–3, 195                   Hofstadter, D. R. 6
                                             Hohlfeld, M. 111, 129
Gagne, P. E. 95                              Holck, H. G. O. 9
Galaburda, A. M. 136, 171, 180–84, 186       Holding, D. H. 8, 29, 32, 35, 41–2, 46, 48,
Galton, F. 171                                 54, 64, 66–7, 87, 95–7, 101–3, 106,
Gardner, H. 46                                 112–14, 120–21, 123, 127, 129, 135,
Gardner, R. A. 9                               181, 194, 200
Gasser, R. U. 21                             Holland, J. H. 6
Gay, J. 7, 117, 177                          Holyoak, K. J. 47
Gelfand, J. J. 23                            Hooper, D. 237
George, M. 119                               Hopkins, B. 7
Gerchak, Y. 181                              Horgan, D. D. 96–8, 104, 106, 173
Geschwind, N. 136, 171, 180–84, 186          Horn, J. 59, 70–71, 80, 151, 176, 178, 188
Gibson, J. J. 48                             Howard, R. W. 47, 150, 172
Gilmartin, K. J. 38, 40–42, 48, 67, 87,      Howe, M. J. A. 136
  100, 202                                   Howes, A. 79
Ginsburg, N. 161                             Hsu, F. H. 14, 28
Glaser, R. 2, 46                             Hu, X. P. 185
Glick, J. A. 7, 117, 177                     Hudson, S. R. 90, 97
Glickman, M. E. 188                          Huffman, C. J. 95
Gobet, F. 8, 25–6, 28, 32, 34, 36–7, 42–6,   Huizinga, J. 5
  48–9, 52–6, 59–62, 64–7, 70, 72–8, 80,     Hunt, E. 8, 99
  83, 87–9, 93–104, 106, 109–10, 115,        Hyde, T. 5
  118–20, 122, 126, 128–9, 134–6, 157–8,     Hyötyniemi, H. 47
  160–62, 166–8, 172, 174–6, 178–81,
  183, 187–8, 191, 196, 201–3, 206,          Iida, H. 1, 91
  249                                        Irvine, S. H. 49
Gold, A. 62, 64, 72, 145, 148, 174           Irving, G. 21
Goldin, S. E. 79, 95–6
Goldstein, H. S. 9                           Jackson, P. 46, 134
Gottret, G. 144, 244                         Jansen, P. J. 21, 24, 44, 101, 126, 166–8,
Grafman, J. 184                                 195
Graham, S. 69                                Jarrell, R. H. 155
Grotzer, T. A. 156                           Jiang, Z. 182
Gruber, H. 61, 64–5, 81, 96, 120, 145,       Joireman, J. A. 178
  148, 174, 201                              Jones, G. 102
256   Author index
Jongman, R. W. 26, 29, 37, 48, 65, 70, 72,    Lasker, Em. 6
  80–83, 96–7, 194, 206                       Lassiter, G. D. 122
Juan, G. 182                                  Laughlin, P. R. 108
                                              Lave, J. 166
Kalakoski, V. 90, 92–3                        Lehmann, A. C. 46
Kämpf, U. 57                                  Leibniz, G. 42, 128
Kareev, Y. 56, 58, 63–4, 70–71, 78, 84, 89,   Levinson, B. M. 9
  116, 137, 197                               Levinson, R. A. 22
Katz, M. J. 150                               Levrier, O. 8
Kawakami, A. 183                              Levy, D. 15, 21
Keane, M. T. 22                               Lewis, D. 74
Keessen, N. R. 91–2                           Leyden, G. 174–6, 188
Keller, B. 63, 96, 177                        Lhôte, J. M. 5
Kelly, E. J. 178                              Li, A. 182
Kennedy, A. 52                                Li, Z. H. 185
Keppel, G. 157                                Lian, M. G. J. 163
Kerwin, J. 19                                 Lipton, R. B. 150
Khalil, R. 8                                  Liptrap, J. M. 159
Kintsch, W. 45–6, 49–50, 93, 98, 103–4,       Lloyd, S. J. 57, 133–4, 199
  122                                         Lockhart, R. S. 95, 103
Kipper, D. A. 178                             Loesch-Berger, M.-C. 63, 96, 146, 176–7
Klahr, D. 48                                  Loomis, E. A. 9
Klein, G. A. 109                              Lories, G. 47, 76, 79, 97, 106
Kmoch, H. 111, 119                            Love, T. 99
Knight, B. 28                                 Lu, B. 28
Knopf, M. 69                                  Lu, P. 14, 21, 28
Koedinger, K. R. 45, 166                      Luria, A. R. 99
Koenig, O. 88                                 Lynn, R. 173–4
Koffka, K. 58
Kogure, T. 183                                McCarthy, J. 8
Kojima, T. 46, 65–6, 109                      McCloskey, L. A. 147
Koltanowski, G. 91–2                          McDermott, J. 46, 110
Kosslyn, S. M. 88                             McEvoy, G. M. 150
Kotov, A. 9, 38, 111, 166–7                   McGregor, S. J. 79
Kotovsky, K. 115                              Mackintosh, N. J. 153, 174
Kraaijeveld, A. R. 5                          Malinowski, B. 5
Krajenbrink, J. 166                           Manowitz, P. 9
Krampe, R. T. 135–6, 156, 168, 171            Margulies, S. 8, 160, 166
Krogius, N. 9, 112, 150, 166                  Markovitch, S. 22, 24
Kronrod, A. 8                                 Marmèche, E. 200
Krulwich, B. 22                               Masunaga, H. 59, 70–71, 80, 151, 176,
Kubat, M. 1, 21, 23, 195                       178, 188
Kuhn, D. 173                                  Mathieu, J. 144
Kuslansky, G. 150                             Matthews, T. D. 95
                                              Mayr, U. 136, 168, 174–5
Laine, T. 98, 134                             Mazur, A. 178
Lake, R. 14, 21, 28                           Medin, D. L. 102
Lancy, D. 140, 148                            Meng, X. M. 185
Lane, D. M. 46, 67, 77–8, 95–6, 101–2,        Michie, D. 18
  119, 175                                    Mieses, J. 91
Lane, P. C. R. 102                            Miletich, R. 184
Lange, R. 108                                 Miller, G. A. 45
Larkin, J. H. 46, 110                         Millis, K. 97–8, 106
Lasker, Ed. 166                               Milojkovic, J. D. 93
                                                                Author index      257
Mireles, D. E. 47, 150                     Pine, J. M. 102
Mitchell, D. H. 63, 71, 73, 83             Pitrat, J. 22, 124, 130, 202
Monty, R. A. M. 52                         Plomin, R. 46
Morgan, D. 96, 104, 173                    Polgar, Zs. 182
Morgenstern, O. 5, 27                      Pomplum, M. 54, 56, 118–19
Mori, N. 115                               Poortinga, Y. 49
Mosenfelder, D. 166                        Popova, A. 163, 237
Moyles, J. R. 155                          Potter, S. 9
Munzert, R. 9, 42, 166                     Poznyanskaya, E. D. 37, 109, 118
Murphy, H. D. 97, 196                      Preussler, W. 69
Murray, H. J. R. 1–2, 5, 181, 237, 244     Purchase, H. 82
                                           Pynte, J. 52
Nado, R. 19
Nakayama, N. 182                           Radach, R. 52
Neimeyer, R. 97–8, 106                     Rappe du Cher, E. 143
Neisser, U. 190                            Ratterman, M. J. 29–30
Newborn, M. 15, 21                         Rayner, E. H. 26, 58, 137, 141, 143, 192,
Newell, A. 15, 25, 32, 37, 39, 42–3, 47,     196, 199
  105, 111, 113–14, 119, 124–5, 128–9,     Redman, T. 157
  134, 202, 207                            Rees, E. 46
N’Guessan Assandé, G. 146, 164–5, 176,     Reingold, E. M. 54, 56–8, 118–19, 199
  199                                      Reitman, J. S. 19, 61–2, 64, 71, 73–4, 78,
Nichelli, P. 184                             203
Nievergelt, J. 65                          Reitman, W. 19
Nunn, J. 21, 195                           Reitman-Olson, J. S. 46
                                           Renkel, A. 201
Odeleye, A. O. 9, 60                       Renkl, A. 145
Oit, M. 94                                 Retschitzki, J. 32, 48, 63, 71, 83, 96, 98,
Oldfield, R. C. 183                           104, 106, 116, 146–8, 151–2, 176–7,
Oliver, I. 102                               179, 196, 206, 237
Oliver, W. 95, 98                          Reurich, L. 6
Onofrj, M. 184                             Rey, M. 8
Opie, I. 140                               Reynolds, R. 41, 72, 113–14, 120–21,
Opie, P. 140                                 123, 125, 173
Opwis, P. 62, 64, 72, 145, 148, 174        Ri, N. 182
                                           Richman, H. B. 66–7, 98, 102, 115,
Paarsalu, M. E. 69                           187
Pachman, L. 9                              Richter, P. 184
Pakenham-Walsh, R. 8                       Riehle, H. J. 184–6
Parker, S. T. 139, 148                     Robbins, T. W. 90, 97, 186
Parlett, D. 237, 245                       Roberts, A. C. 186
Patel, V. L. 49, 104                       Roberts, J. M. 140–42, 148
Peio, K. J. 109                            Robertson, L. 95, 102
Pelletier, J. 8                            Rohrer, D. 60
Pelletier, R. 166                          Röllicke, H.-J. 5
Perkins, D. N. 156                         Romein, J. W. 21
Petkovic, M. 6                             Rosenbloom, P. 134
Petrill, S. A. 46                          Rothöhler, B. 5
Petrowski, N. W. 31, 35–6, 70, 173, 175    Rubin, E. 7, 139, 150, 194
Pfau, H. D. 97, 113, 196                   Rudik, P. A. 31, 35–6, 70, 173, 175
Piaget, J. 33, 47, 133, 138–9, 143–5,      Rudolf, M. 184
  147–8, 152, 158–9, 173
Pierre, C. 143                             Saariluoma, P. 32, 41–3, 47, 49, 57, 66,
Pietrini, P. 184                             73, 76, 78–9, 81–2, 87–8, 90, 92–3,
258   Author index
   97–8, 101, 106, 111, 119–21, 128–9,      Sternberg, R. J. 158
   134, 167, 193, 198–200                   Strobel, R. 57
Saaty, T. L. 173                            Strong, S. M. 8
Sabbagh, G. 8                               Strube, G. 120
Saito, T. 46, 65–6, 82, 109, 114–15, 197    Sturman, M. 23, 195
Salthouse, T. A. 149                        Sutton, R. S. 21
Samuel, A. 21                               Sutton-Smith, B. 5, 140–42, 148
Savina, Y. 123                              Szafron, D. 28
Schädler, U. 5
Schaeffer, J. 14, 21, 28, 119                Tan, S. T. 18
Schneider, W. 145, 148, 174, 201            Tano, J. 163
Schneiderman, B. 69                         Tarrasch, S. 194
Schoen, L. M. 99                            Terekhov, V. A. 37, 110, 198
Schultetus, R. S. 57–8, 121                 Tesauro, G. 14, 21, 23, 29
Schultz, R. 149                             Tesch-Römer, C. 135–6, 156, 171
Schwartz, D. R. 95                          Tesser, A. 97
Schwartz, E. J. 69                          Thagard, P. 24
Scribner, S. 192                            Thomas, A. 184
Scurrah, M. A. 41, 114, 125, 129            Thomson, K. 20–21
Seidel, R. 6                                Thorndike, E. L. 156
Seifert, J. 6                               Thrun, S. 23
Seligman, M. E. P. 179                      Tikhomirov, O. K. 32, 37–8, 109–110,
Selz, Otto 36, 38, 111, 128                   118, 179, 198
Senders, J. W. 52                           Tiss, J. 162
Shaman, D. 84–5, 194                        Townshend, P. 5, 9, 26, 63
Shannon, C. E. 11, 15, 25, 194              Travers, M. W. 156–7, 161, 166
Sharp, D. W. 7, 117, 177                    Treloar, N. 28
Shaw, J. C. 32, 39, 119, 124                Tridgell, A. 22
Shirayanagi, K. 65                          Tulving, E. 95
Shutzman, J. 182                            Turing, A. M. 11, 15
Siebert, F. 6                               Twersky-Lock, E. 23
Siegler, R. S. 142, 146, 152
Simon, D. P. 46, 110                        Uiterwijk, J. W. H. M. 20–21, 24, 108,
Simon, H. A. 1, 7–8, 15, 25–6, 28–9, 32,      195, 202
   37–49, 54, 59–67, 69–70, 72–9, 81–3,
   86–9, 93, 98–102, 104–5, 110–11,         Valentini, G. L. 184
   113–15, 118–20, 122–6, 128–9, 135–6,     van den Herik, H. J. 1, 20, 24, 26
   156, 171, 187, 191, 196–7, 202–3, 206    van der Stoep, A. 5, 91–2
Simonton, D. K. 49, 150                     van Geert, P. 153
Singley, M. K. 156                          van Rijkswijk, J. 20
Skinner, B. F. 166                          Vandenberg, B. 7, 139
Slate, D. J. 113                            Vargas, L. G. 173
Sliwinski, M. 150                           Verghese, J. 150
Sloboda, J. A. 136                          Verhofstadt-Denève, L. 145, 148, 158,
Smilansky, S. 163                             161
Smith, E. E. 102                            Vernoy, M. W. 9
Smith, J. 2, 8                              Vicente, K. J. 49–50, 72, 103–4, 189, 203
Snyder, R. 22                               Vinogradov, Yu E. 37, 179
Stampe, D. M. 54, 56–8, 118–19              Volke, H. J. 184
Starkes, J. L. 69                           von Neumann, J. 5, 27
Staszewski, J. 66, 98, 102, 115, 167, 187
Stefanek, J. 69                             Wagner, D. A. 41, 114, 125, 129
Stefik, M. 46                                Walczak, S. 24
Steinkohl, L. 91                            Walker, R. A. 5
                                                            Author index   259
Wang, J. H. 49–50, 72, 103–4, 189,     Wohl, L. A. 163
 203                                   Wolff, A. S. 63, 71, 73, 83
Wason, P. C. 9, 179, 181               Woodworth, R. S. 156
Waters, A. 72, 100, 146, 172, 174–5,
 188, 196, 201–2                       Xu, T. 182
Watkins, M. J. 95
Watson, P. C. 97                       Yoshikawa, A. 46, 65–6, 82, 109, 114–15,
Weaver, L. 22                            197
Weawer, W. 25
Weiskrantz, L. 186                     Zan, B. 147
Wendling, T. 5                         Zaslavsky, C. 162–3
Wenger, E. 166                         Zermelo, E. 6, 11, 20
Wetzell, R. 167                        Zhang, D. 185
Whyld, K. 237                          Zhang, G. 44
Wienbruch, C. 184–6                    Zhang, X. C. 185
Wilcox, B. 19                          Zhuang, J. 185
Wiles, J. 82                           Ziegler, A. 61, 64–5, 81, 96
Wilkins, D. 124, 130                   Zimmerman, W. S. 175
Wixted, J. T. 60                       Zobrist, A. 18–20
Wober, M. 7                            Zubel, R. 143
Subject index




abstraction 47–8                             archives for experiment design 194
accommodation 47–8                           articulatory loop 90
accuracy 77                                  artificial intelligence 3, 6–8, 13–25, 124,
acquisition of syntax by children 102           202–3
adaptation 47                                artificial-intelligence models relevant to
adaptive intelligence 139                       the psychology of search 124
adult intelligence in chess 173–4            assimilation 47–8
adult intervention 139                       atari 59
adult visuo-spatial abilities in chess 175   attack detection 57–9, 66
advanced-level coaching 165–8                automata 11
adversarial problem solving 25               automatism 57
advertising 5                                awele 1, 4, 15–16, 59, 96, 98, 146–7; and
advisors 24                                     age-related decline 151; concepts from
ageing 149–52; chess 149–50; other              cross-cultural psychology 32;
   games 151–2; see also learning,              description of 240–42; and education
   development, and ageing                      164; move choice 116; mutational and
aggression 142                                  computational complexity 26–7;
‘aha’ experience 115                            problems test 146; skill effect 71;
AI see artificial intelligence                   solution of 21; structure of search in
algorithms 11–12                                106; visuo-spatial abilities in 176–7;
alinement games 3–4, 240                        volatility 63, 83
allergies 180                                awele problems test 146, 177
alpha-beta algorithm 15                      ayo 9, 59–60
ambiguity 63
analogy formation in novice players 123      back-propagation 23
analysis of archives and databases 194–5     backgammon 3, 14, 21, 180, 206, 237
ancientness 149                              backward search 110–11
Anglo-Saxon psychology 128                   backwards induction 6
annotation 119                               ball games 138
anticipation 116, 144                        bao 1, 3–4, 9, 26–7, 71, 77–8; and age-
apperception 32, 42, 93, 128                   related decline 151; blindfold play
apperception-restructuring theory 32,          94–5; clubs in Zanzibar 136;
   42–3                                        comparison with chess 26; concepts
archives and databases (creation and use       from cross-cultural psychology 32;
   of) 192–5; analysis of archives and         description of 242; and education 164;
   databases 194–5; impact on masters’         evaluating positions 116; game
   play 192–3; notational systems 192–3;       specificity 190; and mnemonics 99;
   role of archives for designing              mutational and computational
   experiments 194                             complexity 26–7; recall experiment 71,
262    Subject index
   95; selective search 108; skill effect 66,   board games and mnemonics 99
   100; structure of search in 106;            board games and neuroscience 180–86;
   undoing moves 84–6; volatility 63, 71,        brain activity in chess and Go 183–6;
   83, 107, 117                                  effects of brain lesions on chess skill
basic instruction 163–5                          183; gender differences in chess 181;
Belgian study 158–9                              gender differences in other board
Berlin Structural Model of Intelligence          games 181–2; handedness and chess
   Test 174–5                                    182–3; theory of the neurobiology of
binary decision 26                               chessplaying 180–81
Binet’s studies of blindfold chess 33–4        board games (other than chess) 32, 62–3,
Bingo 162                                        83–4, 94–5; and ageing 151–2;
biological age 149                               education and training 162–3; gender
bits 26                                          differences in 181–2; intelligence and
BKG 14                                           visuo-spatial abilities in 176–7;
blindfold bao 94–5                               macrostructure of search in 106–8;
blindfold chess 1, 31, 33–4, 82, 91–5,           qualitative aspects of search in 114–17
   103–4, 122                                  board games in psychology 6–9; board
blindfold draughts 91–2, 95                      games in clinical and biological
blindfold Go 91                                  psychology 8–9; criticisms of relevance
blindfold playing 90–95; blindfold chess         of board games for psychology 8;
   1, 31, 33–4, 82, 91–5, 103–4; efficacy of       features of board games of relevance
   167; empirical data 92–5; informal            for psychology 7
   accounts 91–2; representations used in      board games in science 5–6; history 5;
   91–5                                          mathematics 6; philosophy 6; social
blindfold shogi 91–2                             science 5–6
blindfold trictrac 91                          board position memory 70–81
board-game complexity 205–6                    bounded rationality 32, 38
board game instruction 156–63;                 brain activity 183–6
   empirical evidence from chess 157–62;       brain lateralization 180
   other board games 162–3; question of        brain lesions and effects on skill 183
   transfer 156–7                              brain-imaging techniques 184, 186, 200,
board game rules 237–47                          207
Board Games in Academia 49                     branching factor 12, 18, 21, 26
board games and clinical and biological        bridge 2, 69, 148, 245
   psychology 8–9; popular psychology 9;       Bronx study 160–61
   psychiatry, psychoanalysis, and             Brooklyn study 161
   psychotherapy 8–9; psychophysiology         brute-force approach 11, 14, 29–30, 202
   9                                           brute-force search 17, 20
board games and cognitive psychology
   2–4; classification of board games 3–4;      calculus 156
   definition of board games 2; knowing:        California Test of Mental Maturity 141
   degree, time, and context 2–3;              capture 237
   organizations 4                             card games 2, 69, 138–40, 245
board games in computer science and            Carnegie Tech 32, 38–41
   artificial intelligence 13–25; computer      case-based planning 22
   databases and retrograde analysis           case-based reasoning 22
   20–21; computers as world champions         CASTLE 22
   14–15; elements of computer search          categorical syllogism 34
   15–16; evaluation functions 16–17;          categorization experiments 65
   machine learning 21–4; opponent             categorization and perception 51–68
   modelling 24–5; philosophical               change-blindness paradigm 56
   implications 25; role of knowledge in       chaos 82
   computer games 17–20; state of the art      characteristics of selected board games
   14–15                                         238–9
                                                                 Subject index    263
chase 138                                    children’s preferences 140
cheating 9                                   Chinese chess see shang qi
check-detection task 56                      Chinook 14, 21, 28–9
checkers 4, 7, 9, 14, 107, 140, 147; and     choice-of-move task 200
  age-related decline 151; computer          CHREST 22, 44–8, 54–5, 66–7, 72,
  program learning techniques 23;               99–103, 134–8, 152; see also EPAM
  description of 242–3; evaluating              theory
  positions 116; informal approaches to      CHUMP 22, 44, 101, 125–6
  training 165; notational archive           chunk construction 134
  systems 192; solution of 21; strategy      CHUNKER 18
  changes 194                                chunking 7, 25–6, 63; evidence for 60
chess 1, 3–6, 10, 31–45, 81–2, 144–6; and    chunking theory 26, 32, 39–43, 46, 59, 66;
  advertising 5; and ageing 149–52;             discussion 99–103; parameters 78
  brain activity in 183–6; brute-force       classification of board games 3–4, 237
  approach 14; complexity landscape of       Cleveland and the development of skill
  206; description of 243–4; drosophila         34–5
  of psychology 8; effects of brain           coaches 167–8
  lesions on skill 183; evaluation times     coaching at an advanced level 165–8;
  116–17; evidence for perceptual               formal approaches 166–7; informal
  chunks in 60–62; expertise in 31–2;           approaches 165–6; media of
  gender differences in 181; general level       instruction 167–8
  of intelligence 47; handedness and         code 245
  182–3; intelligence in 173–4;              coding systems 26
  interference task 77; intuition in 47;     cognition 32, 43, 142, 205
  machine learning 22–3;                     cognitive mechanisms 73
  macrostructure of search in 105–6,         cognitive psychology 2–4, 7, 33, 43, 50,
  129; memory 103, 189, 194; and                72, 128, 190, 197, 204
  military science 5; mutational and         combinatorial analysis 6
  computational complexity 26–7;             combinatorial game theory 23
  opponent modelling 25; and politics 5;     competent dispatch rank order 141
  qualitative aspects of search in           complexity analysis 26–7
  108–14; recall of sequences of moves       complexity landscape of chess 206
  and games 81–2, 90; recognition            computational complexity 26
  experiment 79; representations used in     computational modelling 202–3
  blindfold play 92–4; research into         computer databases and retrograde
  expertise in 31–2; retrieval structures       analysis 20–21
  102; role of knowledge in computer         computer programs for coaching
  games 17–18; role in psychiatric              167–8
  treatment 8; simplified version 143–4;      computer science 2–3, 6–7, 13–25
  skill effect 73; solution of 21; theories   computer simulations 202–3
  of chess skill 33–45; theory of            computers as world champions 14–15
  neurobiology of 180–81; undoing            concentration 116, 162
  moves 84; visuo-spatial abilities in       concept of error 27–8
  174–5; world champion defeat 14; see       concept formation task 102
  also blindfold chess; pseudo-chess         concept identification 108
chess automata 11                            concepts in Go 65–6
chess psychology 38                          conceptual knowledge 101, 119
chess rankings 112, 151, 182                 concrete operational thought 145
Chess 4.5 program 113                        concurrent verbal reports 197
chessplayers’ ethnology 5                    configurations 3
chessplayers’ thinking 43, 105               confirmatory scan 56
chessplaying children 96                     conflict 5
child intelligence in chess 173              connect-four 21, 155
child visuo-spatial abilities in chess 174   connectionism 33, 47
264   Subject index
constraint-attunement theory 50, 72,        die see dice
   103–4                                    Differential Aptitude Test 158
constructive play 139                       differential recall 103
contents analysis 128                       digit-span task 102, 145
context 64                                  directing knowledge 17
contextual information 95–6                 directionality of search 110–11
continuation 58–9                           disability 163
cooperation 48                              discrimination net 40–41, 43–4, 54
coordination 19                             distortion 87, 199
criticisms of relevance of board games      Djakow, Petrowski, and Rudik: in search
   for psychology 8                           of mental abilities 35–6
cross-cultural aspects of methodology       domain content 130
   192                                      domain-free memory skills 56
cross-cultural psychology 32, 49, 84        domain-free perceptual skills 56
cross-sectional skill comparisons 201       domain-specific knowledge 33, 70, 145,
crystallized intelligence 149                 166
                                            dominoes 2, 245
D2 tests 158                                Don’t Spill the Beans 162
dakon 15, 107–8                             draughts 3, 84, 91–2, 151, 164–6, 192–3;
de Groot: selective search and perceptual     description of 242–3
  knowledge 36–7                            drosophila 8
debugging 22                                dungeons and dragons 160
deceit 9                                    duru 94, 190
decentration 48                             dynamic evaluation 116
decision making 2, 5, 105–32                dynamic threat 15
decomposition 61, 116, 126, 166             dyslexia 180
Deep Blue 14, 25, 28–9, 202
Deep Fritz 14                               early death 150
Deep Junior 15                              early stages of learning 133–8; from
deep processing 79                             amateur to master 135–6; learning
definition of board games 2                     pegity and gomoku 136–7; learning
definitions of expertise 187–9; informal        the rules of pseudo-chess 133–4;
  definitions of 188–9; titles and ratings      training novices to memorize chess
  188                                          positions 134–5
Degree of Reading Power Test 160            ecological validity 189–91, 204
degree, time, and context 2–3               Edinburgh Handedness Inventory 183
deliberate practice 45, 135–6               education and training 155–70; board
depression 179                                 game instruction and transfer of skill
depth of search 126, 135                       156–63; teaching the rules and basic
descriptive variables 251–2                    instruction 163–5; training and
destruction of opponent 3                      coaching at an advanced level 165–8
detecting attack 57–9                       effect of ageing on expertise 149
detection-task techniques 198               effects of brain lesions on chess skill 183
development of play and game behaviour      egocentric play 142
  138–40; children’s preferences 140;       egocentrism 48
  Piaget’s conceptions of play 138–40       electroencephalogram 184, 200
development of skill 34–5                   elementary games 141–4
developmental psychology 7                  elements of computer search 15–16
developmental studies 4                     emotions 32, 37, 42, 178–80, 206
developmental studies of specific board      empirical data on role of knowledge in
  games 140–48; elementary games               problem solving 119–23; pattern
  141–4; more complex games 144–7              recognition and search 120–23; role of
developmental theory of Piaget 47–8            schemata and high-level knowledge
dice 2–3                                       119–20
                                                                 Subject index     265
empirical data on role of perception in         of the professional eye 52–4; recent
   problem solving 117–19                       eye-movement studies 56; scanning
empirical data on search behaviour              behaviour in Go and gomoku 56–7;
   105–17; macrostructure of search in          simulating the professional eye with
   chess 105–6; macrostructure of search        CHREST 54–5
   in other games 106–8; qualitative
   aspects of search in chess 108–14;         Factor-Referenced Cognitive Test 175
   qualitative aspects of search in other     fallibility 24
   board games 114–17                         family board games 162
empirical evidence from chess on board        fantasy play 155
   game instruction 157–62; Belgian           feature recognition 59–60
   study 158–9; Bronx study 160–61;           features of board games of relevance for
   Brooklyn study 161; overall evaluation        psychology 7
   161–2; Pennsylvania studies 160; Texas     first-order logic 22–3
   study 159; Zairian study 157–8             fixation 52–5, 118, 183
encoding 42, 46, 73, 76–7, 87, 91–2, 97,      fluid intelligence 149
   119                                        focusing strategy 108
environment 33, 48–9, 55                      formal analyses of board games 11–30;
EPAM theory 40, 48, 66, 102, 149; see            board games in computer science and
   also CHREST                                   artificial intelligence 13–25;
epilepsy 8                                       fundamental concepts 12–13; game
episodic memory 95                               theory and the concept of error 27–8;
equilibrium of forces 46                         information and complexity analysis
error 27–8                                       25–7
erudition 33                                  formal approaches to coaching 166–7
estimation of number of chunks in LTM         formal models on problem solving and
   86–8                                          decision making 129–30
ethnology 5                                   formal orienting condition 96
evaluating positions 112, 116–17              formal thinking 116, 177
evaluation behaviour 112–13                   forward search 110, 129
evaluation functions 16–17, 21, 28, 30        four-in-a-row 15
evaluation knowledge 19                       fox and geese 144, 244
evidence for chunking 60                      Freud’s theory of psychoanalysis 33
evidence for chunks in other board            from amateur to master 135–6
   games 62–3                                 full-width search 17
example of protocol analysis 249–52           fundamental concepts in board game
expectation level 40                             analyses 12–13; game graph 12–13;
expert/novice paradigm 201                       game tree 12
expertise 3–4, 31–2, 42, 69, 87, 103, 247;    fuzziness 33, 91, 126
   in chess 31–2; definitions of 187–9;
   effect of ageing on 149; in Go 59           galvanic skin response 179
expertise paradigm 171                        gambling 2, 9, 182
explicit knowledge 37                         game behaviour 138–40
exploratory scan 56                           game graph 12–13
extraction of descriptive variables           game specificity 189–90
   251–2                                      game theory 5–6, 23, 27–8
extrapolative evaluation 116                  game tree 6, 11–12, 26
eye movements 37, 44, 52–7, 66, 109,          game velocity 141
   117–18, 197–8; and retrospective           games (other than chess) and machine
   protocols 55–6                               learning 23–4
eye-fixation recordings 55, 115                games with rules 138
eye-movement studies 52–7, 66, 152,           games of skill 2
   198–200; eye movements and                 gamesmanship 9
   retrospective protocols 55–6; heuristics   gamma-burst technique 184
266   Subject index
gaze-contingent window paradigm 56,             solution of 21; strategy changes 194;
  197–8                                         see also pegity
gender differences 181–2, 186; in chess        good continuation 58–9
  181; in other board games 181–2             ‘good-enough’ solutions 32
General Aptitude Tests Battery 158            grain size 52, 66
General Problem Solving program 39            guessing experiments 65, 80–82, 142
general theories of cognition 45–7;           Guildford-Zimmerman Spatial
  connectionist accounts 47; general            Visualization Subtest 175
  theories of intelligence and talent
  46–7; knowledge-based theories 46;          hand and finger movements 198
  skilled memory and long-term                handedness 136, 180, 182–3, 186, 200
  working memory 45–6                         hemisphere specialization 183
general theories of intelligence and talent   heuristic search 39
  46–7                                        heuristics 21, 124–8, 130, 195, 202
generic encoding 87                           heuristics of the professional eye 52–4
genetics 46                                   hexapawn 144
genius 49, 51                                 Hi-Q 115
Gestalt principles 24, 58–9                   hide-and-seek 139
Gestalt psychology 37–8, 92                   high-level cognition 43, 62, 65, 67
Go 1, 3–5, 7, 15, 61, 82–3; and age-          high-level knowledge 62, 65, 67, 95–6,
  related decline 151; blindfold 91; brain      103, 119–20
  activity in 183–6; computer program         high-level perception 59–66; additional
  learning techniques 23; concepts in           evidence for perceptual chunks in
  65–6; description of 244; and                 chess 60–62; concepts in Go 65–6;
  education 164; evaluation strategies          evidence for chunking 60; evidence for
  117; expertise in 59; general level of        chunks in other board games 62–3;
  intelligence 47; and gomoku compared          perception in Go and gomoku 63–4;
  63; informal approaches to training           recognizing high-level schemata 65;
  165; interference task 78; intuition in       recognizing key features of a position
  47; knowledge organization of players         rapidly 59–60; some criticisms of the
  46; machine learning 23; main                 concept of perceptual chunks 64–5
  challenge to artificial intelligence 30;     high-level schemata 65
  mutational and computational                history and board games 5
  complexity 26–7; opponent modelling         history heuristic 15
  25; perception in 63–4; recall of           history of board-game psychology 31–3;
  sequences of moves and games 82–3,            other theoretical approaches 33;
  89; recall task 62; recognition               research into expertise in chess 31–2;
  experiment 80; role of knowledge in           research into other board games 32
  computer games 18–20; scanning              Hitech 18
  behaviour in 56–7; search tree 17; skill    Holding’s SEEK theory 41–2, 66
  effect 70, 73; strategy changes 194;         Homo Ludens 5, 10
  visuo-spatial abilities in 176; young       HOYLE 23–4, 29, 207
  children playing 148                        human cognition 205
goals 38                                      hypnotic techniques 37, 179
Gobble 23                                     hypothetico-deductive reasoning 47–8,
Gobet and Simon’s template theory 43–5          177
Gogol 23
gomoku 1, 3, 15, 58, 141; description of      iconic games 139
  245; and Go compared 63; interference       ideal experiment 157
  task 78; learning 136–7; mutational         identifying pieces and detecting attack
  and computational complexity 26–7;             57–9
  perception in 63–4; recall of sequences     Igo Kuraba 182
  of moves and games 89; scanning             illegal deceit 9; see also deceit
  behaviour in 56–7; skill effect 71;          illegality 82, 101
                                                              Subject index    267
illiterate games 190, 198                   knowing: degree, time, and context 2–3
illusion of control 180                     knowledge 19, 69–104; board games and
imaginary scan 57                             mnemonics 99; contextual information
imagination 33                                and high-level knowledge 95–6;
immediate reinvestigation 110                 knowledge and information processing
impact of archiving on masters’ play          97; and memory schemata 95–9;
    193–4                                     retrieval structures 98–9; typicality
impact of board-game research 206–7           97–8; verbal knowledge 96–7
imperfect knowledge 24                      knowledge-based accounts 103
improving spiral 166                        knowledge-based theories 46, 55
incertitude 26                              knowledge in computer games 17–20, 31;
individual differences 171–86                  chess 17–18; Go 18–20
informal approaches to coaching 165–6       kosumi 65
informal definitions of expertise 188–9      Kpelle people 7, 117, 177
informal theories on problem solving and    kroo 59, 116, 146
    decision making 126–9
information analysis 25–6                   lack of control 180
information and complexity analysis         landscape of board games 206
    25–7; complexity analysis of games      latency 57, 60–62, 64, 87, 99, 134–5
    26–7; information analysis of games     laterality of brain activation 185
    25–6                                    lattice 28
information processing 37, 97, 128          learned helplessness 179
information theory 25–6, 194, 202           learning, development, and ageing
innate-talent hypothesis 51                    133–54; ageing 149–52; development
insanity 167                                   of play and game behaviour 138–40;
intelligence 172–8; in chess 173–4;            developmental studies of specific
    discussion of the chess data 175–6;        board games 140–48; early stages of
    mathematical ability 177; other games      learning 133–8; learning rate 205
    176–7; theories 46–7; visuo-spatial     learning pegity and gomoku 136–7
    abilities in chess 174–5                learning rules of pseudo-chess 133–4
inter-individual variability 149            legality 26, 82, 101
interest conflict 27                         life-and-death problems 114–15
interference studies 76–8, 102–3            limited-capacity STM 76, 100–01
internal representation 40, 63              lines of force 54
intervening task 78                         lines-of-action 24
interviews 196                              Logistello 14, 28–9
introspection 34, 196–7                     logistic growth function 74
intuition 25, 47, 129                       long-term memory 39, 43, 45, 72–3, 77,
intuitive experience 37                        86–8, 96, 100–02; in blindfold play
Iowa Test of Basic Skills 141                  92–4; chunks in 134, 149, 202;
Ivory Coast 96, 116, 146, 163                  encoding 87; recall of sequences of
                                               moves and games 81–6
Japanese chess see shogi                    long-term memory storage 186
joseki 20, 83                               long-term working memory 45–6, 50, 90,
Journal of Board Games Studies 49              103, 122; theory 93, 103
Journal of the International Computer       longevity 150
  Games Association 12                      longitudinal studies 201
Jungian personality characteristics 178     look-ahead ability 115, 120, 167, 198
                                            losing move 28
kalah 21                                    lottery games 2
Kalaha 163                                  low-level perception 51–9; eye-movement
key feature recognition 59–60                  studies 52–7; identifying pieces and
killer-move heuristic 15                       detecting attack 57–9
KnightCap 22                                LTM see long-term memory
268   Subject index
machine learning 21–4, 30; chess 22–3;       mental chessboard 98
 Go 23; other games 23–4                     mental imagery 93
machology 6                                  metacognition 173
macrostructure of search in chess 105–6      metaknowledge 24
macrostructure of search in other games      methodology and research designs
 106–8                                         187–204; creation and use of archives
madness 8                                      and databases 192–5; cross-cultural
mahjong 2, 245                                 aspects 192; definitions of expertise
malanj 117                                     187–9; ecological validity 190–91;
mancala games 7, 9, 26, 59–60, 63, 71, 98;     game specificity 189–90; illiterate
 blindfold play 92; calculation of single      games 190; impact of board-game
 move 107; game specificity 189;                research 206–7; interviews and
 potential educational value of 162–4;         questionnaires 196; introspection and
 undoing moves 84–6; volatility 140            retrospection 196–7; mathematical and
Mao’s strategy 5                               computational modelling 202–3;
MAPP 40–42, 67, 87, 99–100                     neuroscientific approaches 200;
mapping 206                                    observations and natural experiments
marbles 138–9                                  196; protocol analysis 197–8; standard
Mastermind 4, 108, 245                         experimental manipulations 198–200;
masters’ play 193–4                            typical research designs 201;
MATER 39, 118, 124–5, 130                      weaknesses and strengths of
mathematical ability 177                       methodologies used in board-game
mathematical and computational                 research 203–4
 modelling 202–3                             micro-awele 163
mathematics and board games 3, 6             mill 21
maximal performance 150                      mimicry 146
meaningful orienting condition 96            Mind Sports Olympiads 4
means-end analysis 39, 42–3                  mind’s eye 40, 44, 54, 88, 126, 167, 198
measures of expertise in board games         minimax algorithm 15, 24–5, 27–8
 247                                         Minnesota Multiphase Personality
media of instruction 167–8                     Inventory 178
memory 33, 61, 64, 66, 69–104, 199–200;      mirror-image reflection 87–8, 99, 103
 for board positions 70–81; capacity         mixed-age interaction 147
 205; discussion 99–104; encoding 42;        mnemonics 33, 77, 94, 99
 estimation of the number of chunks in       mobility strategy 84, 194
 LTM 86–8; for game positions 70–71;         mode of representation 88–91
 knowledge and memory schemata               model organisms 8
 95–9; learning 199–200; limitation 78;      models of heuristic search 39
 load paradigm 90; mechanisms 73;            Monopoly 4, 140, 237
 mode of representation 88–91; recall        moral judgements in children 139
 of sequences of moves and games             more complex games 144–7
 81–6; representations used in blindfold     MORPH 22
 playing 91–5; schemata 95–9; task 60,       motivation 32, 171, 178–80, 191, 206
 66                                          move characteristics 240
memory for board positions 70–81;            move choice phases 109–10, 116
 guessing experiments 80–81;                 move generation 108–9, 114–16
 interference studies 76–8; memory for       move sequences 71
 game positions 70–71; number of             move tree 22–3
 pieces 78; random positions 71–3;           moves in mind 1–2
 recognition experiments 79–80; role of      moving-spot task 94
 presentation time 73–6; standard            mutational complexity 26, 63
 experiment 70–71                            Myers-Briggs Type Indicator 178
Memory Game 162
mental abilities 35–6                        nationality 49
                                                                Subject index     269
natural experiments 196                        computational complexity 26–7; recall
nature of acquisition of knowledge 31          experiment 63; skill effect 71, 73;
neural networks 150, 152, 202                  volatility 73, 83
neural-net learning 21–3                     other theoretical influences in board-
NeuroGoII 23                                   game psychology 33
neuropsychology of talent 171–86; board      oware 240
  games and neuroscience 180–86;
  emotions and motivation 178–80;            PARADISE 124
  intelligence and visuo-spatial abilities   parafoveal vision 119
  172–8; personality 178                     partition 61–4, 81
neuroscience 7, 88, 200, 207                 pattern recognition 22, 28, 30, 40, 42–3,
Nihon Ki-in Joryuukishikai 182                 120–23, 186
nim 143, 148, 245                            pattern-weight pairs 22
nine-men’s morris 20–21, 24                  pegity 3–4, 26, 58, 136–7, 141, 199, 245;
1925 Moscow chess tournament 35, 70,           see also gomoku
  173                                        Pennsylvania studies 160
noise 55, 150                                penny-guessing task 81–2
noncontingency 179                           PERCEIVER 66, 118
nondominant activation 184                   perception 19, 51–68, 117–19, 198, 205–6
nonimmediate reinvestigation 110             perception and categorization 51–68;
nonrehearsal 77                                high-level perception and
nonsense trigrams 77                           categorization 59–66; low-level
nonsymbolic learning technique 23              perception 51–9
normalization 113                            perceptual adaptation underwater 9
notational systems 62, 94; of archiving      perceptual chunks (criticisms of concept
  192–3                                        of) 64–5
novelty heuristic 54                         perceptual chunks in chess 60–62, 64–6,
novelty information 93                         119, 166
novice players and analogy formation         perceptual cues 51
  123                                        perceptual knowledge 36–7
novice players and memorizing chess          perceptual saliency 54, 56
  positions 134–5                            perceptual task 60
NSS 39, 124, 130                             perfect-information games 23–4, 27
null moves 111                               performance 100
number of fields 240                          peripheral vision 118–19
number of pieces 78, 240                     personal contribution of coaches 168
numeric influence function 18, 20             personality 178
numerical aptitude 158, 173                  phases of move choice 109–10, 116
                                             philosophical implications of artificial
objectivity 36                                 intelligence 25
observations 196                             philosophy and board games 6
odu 59–60                                    Piagetian tests 145, 159, 173
Olympics of mind 160                         Piaget’s conceptions of play 138–40
omweso 163                                   Piaget’s theory of cognitive development
operational intelligence 138                   33, 47–8, 140, 158
operations 48                                piece identification 57–9, 66
opponent modelling 24–5, 30                  piece location 72
opponent-model search 24                     planning 111–14
organizations 4                              plasticity of the human mind 46
orientation zone 118                         play 5, 138–40
Othello 14, 23, 63, 84; description of       play behaviour 138–40
  245–6; historical analysis 194; memory     play and games in education 155
  for moves and games 83; move               play tutoring 163
  characteristics 240; mutational and        poker 24
270   Subject index
Polgar sisters 181–2                       psychological tactics 9
polynomial evaluation function 21          psychology and board games 1–10;
popular psychology 9                         board games and cognitive psychology
position decomposition 61                    2–4; moves in mind 1–2; role of board
position evaluation 116–17                   games in psychology 6–9; role of
positional sense 34                          board games in science 5–6
positional strategies 84                   psychology of intelligence 171
positron emission topography 184           psychometric tests 31, 158, 163, 173–5
power law of skill 106, 126                psychophysiology 9
practice play 138                          pure pattern recognition 22
prediction 109, 130                        purpose of the game 237–40
preoperational intelligence 138            puzzles 2
presentation time 70, 73–6, 79, 100,       pygmies 140
  103–4
Primary Mental Abilities Test 158, 174     qualitative aspects of search in chess
primitive strategies 137                     108–14; directionality of search
principles of search 124–5                   110–11; phases of move choice
probability theory 202                       109–10; planning 111–14; progressive
problem solving 10, 105–32, 200, 205;        deepening 110; Reynold’s homing
  analogy formation in novice players        heuristic 114; selective search and
  123; discussion 126–31; empirical data     move generation 108–9
  on role of knowledge in problem          qualitative aspects of search in other
  solving 119–23; empirical data on role     board games 114–17; evaluating
  of perception in problem solving           positions 116–17; phases of move
  117–19; empirical data on search           choice 116; selective search and move
  behaviour 105–17; theoretical              generation 114–16; use of strategies
  accounts 123–6                             and rules 117
problem-solving psychology 127             qualitative organization of knowledge 46
problem-solving task 90, 96, 111, 135,     quantitative amount of knowledge 46
  171, 200                                 question of transfer 156–7
production-system account 40               questionnaires 34, 196
productive thinking 36, 128
professional eye 51–5                      race games 3–4, 237, 240
programmed learning 166                    random positions 70–73
progressive deepening 7, 31, 36, 105,      random-order condition 61
  109–10, 129                              randomization 72, 99, 199
projection ability 17                      randomizer 2, 4
protocol analysis 65, 196–8, 249–52;       ranking system 7
  concurrent verbal reports 197; eye       Ranschburg effect 56
  movements 197–8; hand and finger          ratings 188
  movements 198                            Raven’s Progressive Matrices 173
prototypical play 163                      reaction-time experiments 51
proximity 58–60, 62, 80, 87                real-world applications 207
proximity-based heuristic 134              realism 36
pseudo-chess experiment 57, 133–4          reasoning 200
pseudo-random positions 113                recall 52, 60–62, 81–6
psychiatry, psychoanalysis, and            recall of sequences of moves and games
  psychotherapy 8–9                          81–6; chess 81–2; Go 82–3; other
psycho-galvanic reflex 37                     board games 83–4; undoing moves 84–6
psychological models of search in chess    recall task 60–64, 85, 95
  124–6; CHUMP and SEARCH 125–6;           recent eye-movement studies 56
  models of selective search and           recognition 59, 79–80, 121; of high-level
  principles of search 124–5                 schemata 65; of key features of a
Psychological Research 49                    position 59–60
                                                                 Subject index    271
recognition experiments 79–80                Selzian framework of productive
recognition task 79                             thinking 36, 38, 128
recognition-association assumption 121       semantic long-term memory 39, 43
regression analysis and Elo rating 201       semantic memory 95
relay laps 242                               semantic networks 46
relevance of board games for psychology      semi-dynamic evaluation 116
   7; criticisms of 8                        sensorimotor intelligence 138
repertory grid technique 97                  sensory modality 19
repetition 107                               sequential penny-guessing condition
representations 69–104; mode of 88–91;          82–3
   used in blindfold playing 91–5            shallow threat 195
research designs see methodology and         Shape Memory Test 175
   research designs                          shiang qi 165, 181–2, 192, 243–4
research on genius 49                        shinogi 65
research into expertise in chess 31–2        shogi 4, 15, 91–2, 116, 165, 182, 192,
research into other board games 32              243–4
retrieval structures 45, 71, 73, 79, 98–9,   short-term memory 40, 43, 76–7, 96, 98,
   122                                          100–02, 166–7
retrograde analysis 18, 20–21, 23, 195;      short-term threat 22
   and computer databases 20–21              similarity 58–9
retrospection 196–7                          Simon and the Carnegie Tech group
retrospective protocols 52, 55–6, 62; see       38–41; chunking theory 39–41, 60;
   also verbal protocols                        models of heuristic search 39
revival scan 56                              simplified version of chess 143–4
Reynold’s homing heuristic 110, 114          simulated annealing 23
Rorschach test 158                           simulated eye 44
rote learning 96, 166                        simulation of the professional eye with
roulette 2                                      CHREST 54–5
rules 1, 2, 6, 84, 117, 133–4, 138, 163–5,   simultaneous chess 109, 122, 196
   237–46                                    single photon emission computerized
                                                tomography 184
Saariluoma’s apperception-restructuring      six-in-a-row 240
   theory 42–3                               skat 69
saccade 52                                   skill 33–45, 59, 63, 66, 100, 120
satisficing 39, 105                           skill effect 66, 70–73, 76, 79, 100, 103–4,
scanning behaviour in Go and gomoku             203
   56–7                                      skilled memory 45–6
scepticism 189                               slots 43
schemata 65, 95–9, 103, 119–20               social sciences and board games 5–6
schemata (creation and use of) 43            socio-dramatic play 155
schemes 47                                   solitaire chess 115
schizophrenia 8                              solution 15, 20–21
Scrabble 8                                   sorting task 65
SEARCH 44–5, 125–6, 129, 207                 soufu 164
search algorithms 11, 14–17, 24, 30          Soviet chess psychology 166
search behaviour 105–14                      spatial aptitude 158, 173–4
search extension 14                          speed chess 17, 109, 122–3
search tree 9, 17, 29, 106–8, 110, 114,      standard experimental manipulations
   124, 135                                     198–200; memory 199–200; perception
search-like evaluation 109                      198–9; problem solving and reasoning
SEEK theory 41–2                                200
selective search 7, 36–7, 105, 108–9,        state-space 18, 26
   114–16, 166; models of 124–5              state-space complexity 26
self confidence 36                            static evaluation 116
272   Subject index
STM see short-term memory                    theories of chess skill 33–45; Binet’s
stone configurations 59                          study of blindfold chess 33–4;
strategy development 146                        Cleveland and the development of
strategy use 117, 237                           skill 34–5; De Groot: selective search
stress 150                                      and perceptual knowledge 36–7;
Stroop task 19                                  Djakow, Petrowski, and Rudik: in
Stroop-like interference effect 58, 94           search of mental abilities 35–6; Gobet
structural grammar for analysis of game         and Simon’s template theory 43–5;
   collections 140                              Holding’s SEEK theory 41–2;
subclusters 62                                  Saariluoma’s apperception-
suboptimal moves 24                             restructuring theory 42–3; Simon and
Sungka 163                                      the Carnegie Tech group 38–41;
superclusters 61                                Tikhomirov and colleagues 37–8
SUPREM 18                                    theories of development and
swindling 24                                    environment 47–9; cross-cultural
symbolic learning technique 23                  psychology 49; developmental theory
symbolic play 138, 155                          of Piaget 47–8; role of the
symbolism 34                                    environment 48–9
‘synchronic analysis’ of language 6          theories of intelligence 46–7
system of playing methods 120, 165           theory of deliberate practice 136
                                             theory of mind 24
tactical strategy 108                        theory of neurobiology of chessplaying
tactician 20                                    180–81
tactics 151                                  theory of talent 136
TAL 22                                       thinking aloud 105–6, 200
talent theories 46–7, 136                    thinking processes 205
talent tradition 171                         Thought and Choice in Chess 36
talking chess 55                             threat 15, 22, 109, 195
targets 3                                    three-in-a-row see tic-tac-toe
teaching rules 163–5                         tic-tac-toe 3–4, 7, 12, 23–4, 140–43, 148,
technical contribution of coaches 168           245
template theory 43–5, 59, 65–7;              Tikhomirov and colleagues 37–8
   discussion 99–103                         titles 188
temporal-difference algorithms 23             Torrance test of creative thinking 160
temporal-difference learning 21–3, 29         training and education 155–70; board
tenuki 83                                       game instruction and transfer of skill
terminal knowledge 17                           156–63; teaching the rules and basic
testosterone 178, 180                           instruction 163–5; training and
Texas Learning Index 159                        coaching at an advanced level
Texas study 159                                 165–8
textbooks for coaching 167–8                 training novices to memorize chess
The many faces of Go 19                         positions 134–5
theoretical accounts of problem solving      transfer of skill 156–63
   and decision making 123–6; AI models      trial and error 116
   relevant to psychology of search 124;     trictrac 91
   psychological models of search in         tsume-Go problems 114
   chess 124–6                               tsumi-shogi problems 115
theories of board-game psychology            typical research designs 201
   31–50; brief history of board-game        typicality 78, 97–8
   psychology 31–3; influences from
   other theories of cognition 45–7;         uncertainty 2
   theories of chess skill 33–45; theories   undoing moves 84–6
   of development and environment            universal competence to games 140
   47–9                                      US Chess Federation 182, 188
                                                                  Subject index     273
use of strategies and rules 117                Watson-Glaser Critical Thinking
                                                 Appraisal Test 160
verbal knowledge 96–7                          weaknesses and strengths of
verbal learning behaviour 102                    methodologies used in board-game
verbal protocols 37–9, 52, 62, 81, 96, 109;      research 203–4
   see also retrospective protocols            Wechsler Intelligence Scale for Children
visualization 34, 90–92, 94–5                    161, 173
visuo-spatial abilities 172–8; see also        win-stay and lose-shift hypothesis 114
   intelligence                                winning strategy 141
visuo-spatial memory 40, 44, 90                wisdom 152
volatility 63, 71, 73, 95, 98, 107, 117, 140
                                               Zairian study 157–8
war games 3–4, 237, 240                        zero-sum games 27

				
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Description: Board games have long fascinated as mirrors of intelligence, skill, cunning, and wisdom. While board games have been the topic of many scientific studies, and have been studied for more than a century by psychologists, there was until now no single volume summarizing psychological research into board games. This book, which is the first systematic study of psychology and board games, covers topics such as perception, memory, problem solving and decision making, development, intelligence, emotions, motivation, education, and neuroscience. It also briefly summarizes current research in artificial intelligence aiming at developing computers playing board games, and critically discusses how current theories of expertise fare with board games. Finally, it shows that the information provided by board-game research, both data and theories, have a wider relevance for the understanding of human psychology in general.